2019
15
1
0
215
1

MultiFrame Vectors for Unitary Systems in Hilbert $C^{*}$modules
https://scma.maragheh.ac.ir/article_34968.html
10.22130/scma.2018.77908.356
1
In this paper, we focus on the structured multiframe vectors in Hilbert $C^*$modules. More precisely, it will be shown that the set of all complete multiframe vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multiRiesz vectors, when the surjective operator is replaced by unitary and invertible operators, respectively. Moreover, we show that new multiframes (resp. multiRiesz bases) can be obtained as linear combinations of known ones using coefficients which are operators in a certain class.
0

1
18


Mohammad
Mahmoudieh
School of Mathematics and computer Science, Damghan University, Damghan, Iran.
Iran
mahmoudieh@du.ac.ir


Hessam
Hosseinnezhad
School of Mathematics and computer Science, Damghan University, Damghan, Iran.
Iran
hosseinnezhad_h@yahoo.com


Gholamreza
Abbaspour Tabadkan
School of Mathematics and computer Science, Damghan University, Damghan, Iran.
Iran
abbaspour@du.ac.ir
Multiframe vector
Wandering vector
Local commutant
Unitary system
[[1] S.T. Ali, J.P. Antoine, and J.P. Gazeau, Continuous frames in Hilbert space, Ann. Physics., 222 (1993), pp. 137.##[2] B.K. Alpert, A class of bases in $L^2$ for the sparse representation of integral operators, SIAM J. Math. Anal., 24 (1993), pp. 246262.##[3] L. Arambasic, On frames for countably generated Hilbert $C^*$modules, Proc. Amer. Math. Soc., 135 (2007), pp. 469478.##[4] D. Bakic and B. Guljas, Hilbert $C^*$modules over $C^*$algebras of compact operators, Acta Sci. Math. (Szeged), 68 (2002), pp. 249269.##[5] P. Balazs, M. D"orfler, N. Holighaus, F. Jaillet, and G. Velasco, Theory, implementation and applications of nonstationary Gabor frames, J. Comput. Appl. Math., 236 (2011), pp. 14811496.##[6] P. Balazs, B. Laback, G. Eckel, and W.A. Deutsch, Timefrequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking, IEEE Trans. Audio. Speech. Language Process., 18 (2010), pp. 3449.##[7] J.J. Benedetto and S. Li, The theory of multiresolution analysis frames and applications to filter banks, Appl. Comput. Harmon. Anal., 5 (1998), pp. 389427.##[8] H. B"olcskei, F. Hlawatsch, and H.G. Feichtinger, Frametheoretic analysis of oversampled filter banks, IEEE Trans. Signal Processing., 46 (1998), pp. 32563268.##[9] P. Casazza and G. Kutyniok, Finite Frames: Theory And Applications, Springer Science & Business Media, Birkhauser, 2012.##[10] P.G. Casazza, G. Kutyniok, and S. Li, Fusion frames and distributed processing, Appl. Comput. Harmon. Anal., 254 (2008), pp. 114132.##[11] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, 2016.##[12] O. Christensen and D. Stoeva, $p$frames in separable Banach spaces, Adv. Comput. Math., 18 (2003), pp. 117126.##[13] N. Cotfas and J.P. Gazeau, Finite tight frames and some applications, J. Phys. A., 43 (2010), p. 193001.##[14] S. Dahlke, M. Fornasier, and T. Raasch, Adaptive Frame Methods for Elliptic Operator Equations, Adv. Comput. Math., 27 (2007), pp. 2763.##[15] X. Dai and D.R. Larson, Wandering vectors for unitary systems and orthogonal wavelets, Amer. Math. Soc., 640, 1998.##[16] I. Daubechies, Ten lectures on wavelet, SIAM, Philadelphia, 27, 1992.##[17] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 12711283.##[18] M. Dorfler and H. Feichtinger, Quilted Gabor families I: Reduced multiGabor frames, Appl. Comput. Harmon. Anal., 356 (2004), pp. 20012023.##[19] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341366.##[20] M. Frank and D. Larson, Frames in Hilbert $C^*$modules and $C^*$algebras, J. Operator Theory., 48 (2002), pp. 273314.##[21] D. Gabor, Theory of communication. Part 1: The analysis of information, Journal of the Institution of Electrical EngineersPart III: Radio and Communication Engineering 93 (1946), pp. 429441.##[22] X. Guo, Multiframe vectors for unitary systems, Indian J. Pure Appl. Math., 43 (2012), pp. 391409.##[23] D. Han, Tight frame approximation for multiframes and supperframes, J. Approx. Theory., 129 (2004), pp. 7893.##[24] C. Heil, A Basis Theory Primer, expanded edition. Springer Science & Business Media, 2010.##[25] L. Herve, Multiresolution analysis of multiplicity d: applications to dyadic interpolation, Appl. Comput. Harmon. Anal., 1 (1994), pp. 299315.##[26] W. Jing, Frames in Hilbert $C^*$modules, Ph.D. Thesis, University of Central Florida, 2006.##[27] E.C. Lance, Unitary operators on Hilbert $C^*$modules, Bull. Lond. Math. Soc., 26 (1994), pp. 363366.##[28] E.C. Lance, Hilbert $C^*$modules: A Toolkit for Operator Algebraists, Cambridge University Press, Cambridge, 1995.##[29] S.Q. Liu, H.L. Jin, X.O. Tang, H.Q. Lu and S.D. Ma, Boosting multiGabor subspaces for face recognition, In: Asian Conference on Computer Vision. Springer, Berlin, Heidelberg, 2006, 539548.##[30] P. Majdak, P. Balazs, W. Kreuzer, and M. Dorfler, A timefrequency method for increasing the signaltonoise ratio insystem identification with exponential sweeps, In: Proceedings of the 36th International Conference on Acoustics, Speech and Signal Processing, ICASSP 2011, Prag, 2011, 38123815.##[31] V.M. Manuilov and E.V. Troitsky, Hilbert $C^*$modules, Amer. Math. Soc., 2005.##[32] R. Stevenson, Adaptive solution of operator equations using wavelet frames, SIAM J. Numer. Anal., 41 (2003), pp. 10741100.##]
1

A Generalization of the MeirKeeler Condensing Operators and its Application to Solvability of a System of Nonlinear Functional Integral Equations of Volterra Type
https://scma.maragheh.ac.ir/article_34954.html
10.22130/scma.2018.74869.322
1
In this paper, we generalize the MeirKeeler condensing operators via a concept of the class of operators $ O (f;.)$, that was given by Altun and Turkoglu [4], and apply this extension to obtain some tripled fixed point theorems. As an application of this extension, we analyze the existence of solution for a system of nonlinear functional integral equations of Volterra type. Finally, we present an example to show the effectiveness of our results. We use the technique of measure of noncompactness to obtain our results.
0

19
35


Shahram
Banaei
Department of Mathematics, Bonab Branch, Islamic Azad University, Bonab, Iran.
Iran
sh_banaei@yahoo.com


Mohammad Bagher
Ghaemi
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
Iran
mghaemi@iust.ac.ir
Measure of noncompactness
Fixed point theorem
Integral equations
[[1] R. Agarwal, M. Meehan, and D. O'Regan, Fixed point theory and applications, Cambridge University Press, 2004.##[2] A. Aghajani, J. Banas, and Y. Jalilian, Existence of solution for a class nonlinear Voltrra sigular integral, Appl. Math. Comput., 62 (2011), pp. 12151227.##[3] A. Aghajani, M. Mursaleen, and A. Shole Haghighi, Fixed point theorems for MeirKeeler condensing operators via measures of noncompactness, Acta Mathematica Scientia., 35 (2015), pp. 552566.##[4] I. Altun and D. Turkoglu, A fixed point theorem for mappings satisfying a general contractive condition of operator type, Journal of Computational Analysis and Applications., 9 (2007), pp. 914.##[5] R. Arab, R. Allahyari, and A. Shole Haghighi, Construction of a Measure of Noncompactness on BC($Omega$) and its Application to Volterra Integral Equations, Mediterr. J. Math., 13 (2016), pp. 11971210.##[6] Sh. Banaei, M.B. Ghaemi, and R. Saadati, An extension of Darbo's theorem and its application to system of neutral diferential equations with deviating argument, Miskolc Mathematical Notes, 18 (2017), pp. 8394.##[7] J. Banas, M. Jleli, M. Mursaleen, and B. Samet, Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness, Springer, Singapore, 2017.##[8] J. Banas and K. Goebel, Measures of noncompactness in Banach spaces, Lecture Notes in Pure and Applied Mathematics, New York, 1980.##[9] J. Banas, D. O'regan, and K. Sadarangani, On solutions of a quadratic hammerstein integral equation on an unbounded interval, Dynam. Systems Appl., 18 (2009), pp. 251264.##[10] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova., 24 (1955), pp. 8492.##[11] M.A. Darwish, Monotonic solutions of a convolution functional integral equation, Appl. Math. Comput., 219 (2013), pp. 1077710782.##[12] V. Karakaya, N. El Houda Bouzara, and Y. Atalan, Existence of tripled fixed points for a class of condensing operators in banach spaces, The Scientific World Journal, (2014), pp. 19.##[13] K. Kuratowski, Sur les espaces, Fund. Math., 15 (1930), pp. 301309.##[14] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math Anal Appl., 28 (1969), pp. 326329.##[15] M. Mursaleen and S.A. Mohiuddine, Applications of measures of noncompactness to the infinite system of differential equations in $l_p$ spaces, Nonlinear Analysis., 75 (2012), pp. 21112115.##[16] L. Olszowy, Solvability of infinite systems of singular integral equations in Frechet space of continuous functions, Computers and Mathematics with Applications, 59 (2010), pp. 27942801.##[17] A. Samadi and Mohammad B. Ghaemi, An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations, Filomat., 28 (2014), pp. 879886.##[18] B. Samet, Coupled fixed point theorems for a generalized MeirKeeler contraction in partially ordered metric spaces, Nonlinear Analysis, 72 (2010), pp. 45084517.##]
1

Controlled Continuous $G$Frames and Their Multipliers in Hilbert Spaces
https://scma.maragheh.ac.ir/article_34963.html
10.22130/scma.2019.68582.264
1
In this paper, we introduce $(mathcal{C},mathcal{C}')$controlled continuous $g$Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$controlled continuous $g$frames is a $(mathcal{C},mathcal{C}')$controlled continuous $g$frame. Also, we investigate when a $(mathcal{C},mathcal{C}')$controlled continuous $g$Bessel multiplier is a pSchatten class operator.
0

37
48


Yahya
Alizadeh
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 5619911367, Iran.
Iran
ya.alizadeh@gmail.com


Mohammad Reza
Abdollahpour
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 5619911367, Iran.
Iran
mrabdollahpour@yahoo.com
Controlled continuous $g$frames
$(mathcal{C}
mathcal{C}')$controlled continuous $g$Bessel families
Multiplier of continuous $g$frames
[[1] M.R. Abdollahpour and Y. Alizadeh, Multipliers of Continuous $G$Frames in Hilbert spaces, Bull. Iranian. Math. Soc., 43 (2017), pp. 291305.##[2] M.R. Abdollahpour and M.H. Faroughi, Continous gFrames in Hilbert spaces, Southeast asian Bulletin of Mathematics, 32 (2008), pp. 119.##[3] P. Balazs, Basic definition and properties of Bessel multipliers, J. Math. Anal. Appl., 325 (2007), pp. 571585.##[4] P. Balazs, J.P. Antoine, and A. Grybos, Weighted and controlled frames, Int. J. Wavelets Multiresolut Inf. Prosses., 8 (2010), pp. 109132.##[5] P. Balazs, D. Bayer, and A. Rahimi, Multipliers for continuous frames in Hilbert spaces, J. Phys. A: Math. Theory., 45 (2012), pp. 120.##[6] I. Bogdanova, P. Vandergheynst, J.P. Antoine, L. Jacques, and M. Morvidone, Stereographic wavelet frames on sphere, Applied Comput. Harmon. Anal., 19 (2005), pp. 223252.##[7] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser Boston, 2003.##[8] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier seris, Trans. Amer. Math. Soc., 72 (1952), pp. 341366.##[9] L.O. Jacques, Reperes et couronne solaire, These de Doctorat, Univ. Cath. Louvain, LouvainlaNeuve. 2004.##[10] G.J. Murphy, $C^*$algebras and operator theory, Academic Press Inc., 1990.##[11] A. Rahimi and A. Fereydooni, Controlled $G$Frames and Their $G$Multipliers in Hilbert spaces, An. St. Univ. Ovidius Constanta, versita., 21 (2013), pp. 223236.##[12] W. Sun, Gframes and gRiesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437452.##]
1

Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem
https://scma.maragheh.ac.ir/article_34964.html
10.22130/scma.2018.74791.321
1
In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D timedependent initialboundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function and a sevenfold 3D wavelet and all of our computations are based on this new set to approximate in 3D spatial. Moreover, approximation in time domain is based on finite difference method. By substitution in the 3D DPL model, the differential equation converts to a linear system of equations and related system is solved directly. We use the LaxRichtmyer theorem to investigate the consistency, stability and convergence analysis of our method. Numerical results are presented and compared with the analytical solution to show the efficiency of the method.
0

49
63


Zahra
Kalateh Bojdi
Department of Mathematics, Faculty of Science and New Technologies, Graduate University of Advanced Technology, Kerman, Iran.
Iran
z.kalatehbojdi@student.kgut.ac.ir


Ataollah
Askari Hemmat
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman,
Kerman, Iran.
Iran
askari@uk.ac.ir


Ali
Tavakoli
Mathematics department, University of Mazandaran, Babolsar, Iran.
Iran
a.tavakoli@umz.ac.ir
MRA
Heat equation
wavelet method
Finite difference
[[1] G. Beylkin, Wavelets and Fast Numerical Algorithms, Lecture Notes for Short Course, Amer. Math. Soc., Rhode Island, 1993.##[2] G. Beylkin and N. Saito, Wavelets, their autocorrelation functions, and multiresolution representation of signals, Expanded abstract in Proceedings ICASSP92, 4 (1992), pp. 381384.##[3] C. Canuto, M.Y. Hussaini, A. Quarteroni, and Th.A. Zang, Spectral Methods: Fundamentals in Single Domains, Berlin, Springer, 2006.##[4] C. Canuto, M.Y. Hussaini, A. Quarteroni, and Th.A. Zang, Spectral Methods in Fluid Dynamics, Berlin, Springer Series in Computational Physics, 1988.##[5] G. Chen, Semianalytical solutions for 2D modeling of long pulsed laser heating metals with temperature dependent surface absorption, Optik, International Journal for Light and Electron Optics, 2017.##[6] RJ. Chiffell, On the wave behavior and rate effect of thermal and thermomechanical waves, M.Sc. Thesis, University of New Mexico, Albuquerque, 1994.##[7] W. Dai, F. Han, and Z. Sun, Accurate Numerical Method for Solving DualPhaseLagging Equation with Temperature Jump Boundary Condition in Nano Heat Conduction, Int. J. Heat Mass Transf., 64 (2013), pp. 966975.##[8] W. Dai and R. Nassar, A compact finite difference scheme for solving a onedimensional heat transport equation at the microscale, J. Comput. Appl. Math., 132 (2001), pp. 431441.##[9] W. Dai and R. Nassar, A compact finite difference scheme for solving a threedimensional heat transport equation in a thin film, Numer. Methods Partial Differ. Equ., 16 (2000), pp. 441458.##[10] W. Dai and R. Nassar, A finite difference method for solving the heat transport equation at the microscale, Numer. Methods Partial Differ. Equ., 15 (1999), pp. 697708.##[11] W. Dai and R. Nassar, A finite difference scheme for solving a threedimensional heat transport equation in a thin film with microscale thickness, Internat. J. Numer. Methods Engrg., 50 (2001), pp. 16651680.##[12] I. Daubechies, Ten Lectures on Wavelets, Soc. for Indtr. Appl. Math., Philadelphia, Number 61, 1992.##[13] J. Fan and L. Wang, Analytical theory of bioheat transport, J. Appl. Phys., 109 (2011).##[14] ZY. Guo and YS. Xu, NonFourier Heat Conduction in IC Chip, ASME J. Electron Packag., 117 (1995), pp. 174177.##[15] Z. Kalateh Bojdi and A. Askari Hemmat, Wavelet collocation methods for solving the Pennes bioheat transfer equation, Optik, Int. J. Light Electron Optics, 132 (2017), pp. 8088.##[16] Z. Kargar and H. Saeedi, Bspline wavelet operational method for numerical solution of timespace fractional partial differential equations, Int. J. Wavelets Multiresolut. Inf. Process., 15 (2017), 1750034.##[17] A. Latto, L. Resnikoff, and E. Tenenbaum, The evaluation of connection coefficients of compactly supported wavelets, Proceedings of the FrenchUSA Workshop on Wavelets and Turbulence, 1992, pp. 7689.##[18] A. Malek, Z. Kalateh Bojdi, and P. Nuri Niled Gobarg, Solving Fully threeDimensional Micros cal Dual Phase Lag Problem Using MixedCollocation, Finite Difference Discretization, Trans. ASME J. Heat Transf., 134 (2012).##[19] A. Malek and SH. MomeniMasuleh, A Mixed CollocationFinite Difference Method for 3D Microscopic Heat Transport Problems, J. Comput. Appl. Math., 217 (2008), pp. 137147.##[20] A. Malek and S.H. MomeniMasuleh, A Mixed CollocationFinite Difference Method for 3D Microscopic Heat Transport Problems, J. Comput. Appl. Math., 217 (2008), pp. 137147.##[21] S. Mallat, Multiresolution approximation and wavelets, Preprint GRASP Lab., Dept. of Computer and Information Science, Univ. of Pennsylvania, 1987.##[22] T.Q. Qui and C.L. Tien, Shortpulse laser heating on metals, Int. J. Heat Mass Transf., 35 (1992), pp. 719726.##[23] T.Q. Qui and C.L. Tien, Heat transfer mechanisms during shortpulse laser heating on metals, ASME J. Heat Transf., 115 (1993), pp. 835841.##[24] G.D. Smith, Numerical Solution of Partial Differential Equations Finite Difference Methods, Third ed., Oxford, Oxford University Press, 1985.##[25] D.Y. Tzou, Macro to Micro Heat Transfer, Washington, Taylor and Francis, 1996.##[26] R. Viskanta and T.L. Bergman, Heat Transfer in Materials Processing, Third Edition, New York, McGrawHill Book Company, 1998.##[27] D. Xue, Threedimensional simulation of the temperature field in highpower doubleclad fiber laser, Optik, Int. J. Light Electron Optics, (2011).##[28] J. Zhang and J.J. Zhao, Iterative solution and finite difference approximations to 3D microscale heat transport equation, Math. Comput. Simulation, 57 (2001), pp. 387404.##]
1

Theory of Hybrid Fractional Differential Equations with Complex Order
https://scma.maragheh.ac.ir/article_34967.html
10.22130/scma.2018.72907.295
1
We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$ Lipschitzian and the other one is completely continuous, we prove the existence of mild solutions of initial value problems for hybrid fractional differential equations. Finally, an application to solve onevariable linear fractional Schr"odinger equation with complex order is given.
0

65
76


Devaraj
Vivek
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore641020, India.
Iran
peppyvivek@gmail.com


Omid
Baghani
Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
Iran
omid.baghani@gmail.com


Kuppusamy
Kanagarajan
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore641020, India.
Iran
kanagarajank@gmail.com
Hybrid fractional differential equations
Initial value problem
Complex order
Dhage's fixed point theorems
Existence of mild solution
[[1] B. Ahmad and S.K. Ntouyas, An existence theorem for fractional hybrid differential inclusions of hadamard type with Dirichlet boundary conditions, Abstr. Appl. Anal., (2014), Article ID 705809, 7 pages.##[2] B. Ahmad and S.K. Ntouyas, Initial value problems for hybrid Hadamard fractional differential equations, Electron. J. Diff. Eq., 161 (2014), pp. 18.##[3] R. Andriambololona, R. Tokiniaina, and H. Rakotoson, Definitions of complex order integrals and complex order derivatives using operator approach, Int. J. Latest Res. Sci. Tech., 1 (2012), pp. 317323.##[4] T.M. Atanackovic, S. Konjik, S. Pilipovic, and D. Zorica, Complex order fractional derivatives in viscoelasticity, Mech. TimeDepend. Mater., 1 (2016), pp. 121.##[5] O. Baghani, On fractional Langevin equation involving two fractional orders, Commun. Nonlinear##Sci. Numer. Simulat., 42 (2017), pp. 675681.##[6] B.C. Dhage, On a fixed point theorem in Banach algebras with applications, Appl. Math. Lett., 18 (2005), pp. 273280.##[7] B.C. Dhage, On some variants of Schauder's fixed point principle and applications to nonlinear integral equations, J. Math. Phys. Sci., 25 (1988), pp. 603611.##[8] B.C. Dhage and V. Lakshmikantham, Basic results on hybrid differential equations, Nonlinear Anal. Hybrid Syst., 4 (2010), pp. 414424.##[9] P. Gorka, H. Prado, and J. Trujillo, The time fractional Schr"odinger equation on Hilbert space, Integr. Equ. Oper. Theory, 88 (2017), pp. 114.##[10] M.A.E. Herzallah and D. Baleanu, On fractional order hybrid differential equations, Abst. Appl. Anal., 2014, Article ID 389386, 7 pages.##[11] R. Hilfer, Application of Fractional Calculus in Physics, World Scientific, Singapore, 1999.##[12] A.A. Kilbas, H.M. Srivasta, and J.J. Trujillo, Theory and Application of Fractional Differential Equations, Elsevier B. V., Netherlands, 2016.##[13] N. Kosmatov, Integral equations and initial value problems for nonlinear differential equations of fractional order, Nonlinear Anal., 70 (2009), pp. 25212529.##[14] E.R. Love, Fractional derivatives of imaginary order, J. London Math. Soc., 2 (1971), pp. 241259.##[15] A. Neamaty, M. Yadollahzadeh, and R. Darzi, On fractional differential equation with complex order, Progr. Fract. Differ. Appl., 1 (2015), pp. 223227.##[16] C.M.A. Pinto and J.A.T. Machado, Complex order Van der Pol oscillator, Nonlinear Dyn., 65 (2011), pp. 247254.##[17] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.##[18] B. Ross and F. Northover, A use for a derivative of complex order in the fractional calculus, Int. J. Pure Appl. Math., 9 (1978), pp. 400406.##[19] S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, Philadelphia, 1993.##[20] D. Vivek, K. Kanagarajan, and S. Harikrishnan, Dynamics and stability results for integrodifferential equations with complex order, Discontinuity, Nonlinearity and Complexity, In Press, 2018.##[21] D. Vivek, K. Kanagarajan, and S. Harikrishnan, Dynamics and stability results for pantograph equations with complex order, Journal of Applied Nonlinear Dynamics, 7 (2018), pp. 179187.##[22] Y. Zhao, S. Sun, Z. Han, and Q. Li, Theory of fractional hybrid differential equations, Comput. Math. Appl., 62 (2011), pp. 13121324.##]
1

$sigma$Connes Amenability and Pseudo(Connes) Amenability of Beurling Algebras
https://scma.maragheh.ac.ir/article_34969.html
10.22130/scma.2018.73939.308
1
In this paper, pseudoamenability and pseudoConnes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudoConnes amenability and pseudoamenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.
0

77
89


Zahra
Hasanzadeh
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Iran
zh_hasanzadeh@yahoo.com


Amin
Mahmoodi
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Iran
a_mahmoodi@iauctb.ac.ir
$sigma$Connes amenability
Pseudoamenability
PseudoConnes amenability
Beurling algebras
[[1] H.G. Dales, Banach algebras and automatic continuity, Clarendon Press, Oxford, 2000.##[2] H.G. Dales and A. T.M. Lau, The second duals of Beurling algebras, American Mathematical Society, 2005, no 836.##[3] M. Daws, Connesamenability of bidual and weighted semigroup algebras, Math. Scand., 99 (2006), pp. 217246.##[4] G.H. Esslamzadeh, B. Shojaee, and A. Mahmoodi, Approximate Connesamenability of dual Banach algebras, Bull. Belgian Math. Soc. Simon Stevin, 19 (2012), pp. 193213.##[5] F. Ghahramani and R.J. Loy, Generalized notions of amenability, J. Funct. Anal., 208 (2004), pp. 229260.##[6] F. Ghahramani, R.J. Loy, and Y. Zhang, Generalized notions of amenability, II, J. Funct. Anal., 254 (2008), pp. 17761810.##[7] F. Ghahramani and Y. Zhang, Pseudoamenable and pseudocontractible Banach algebras, Math. Proc. Camb. Phil. Soc., 142 (2007), pp. 111123.##[8] B. E. Johnson, Approximate diagonals and cohomology of certain annihilator Banach algebras, Amer. J. Math., 94 (1972), pp. 685698.##[9] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972), pp. 196.##[10] A. Mahmoodi, Approximate injectivity of dual Banach algebras, Bull. Belgian Math. Soc. Simon Stevin., 20 (2013), pp. 112.##[11] A. Mahmoodi, Bounded approximate Connesamenability of dual Banach algebras, Bull. Iranian Math. Soc., 41 (2015), pp. 227238.##[12] A. Mahmoodi, Connesamenabilitylike properties, Studia Math., 220 (2014), pp. 5572.##[13] M. Mirzavaziri and M. S. Moslehian, $sigma$amenability of Banach algebras, Southeast Asian Bull. Math., 33 (2009), pp. 8999.##[14] M. Mirzavaziri and M. S. Moslehian, $sigma$derivation in Banach algebras, Bull. Iranian Math. Soc., 32 (2006), pp. 6578.##[15] M.S. Moslehian and M.N. Motlagh, Some notes on $(sigma, tau)$amenableof Banach algebras, Stud. Univ. BabesBolyai Math., 53 (2008), pp. 5768.##[16] V. Runde, Amenability for dual Banach algebras, Studia Math., 148 (2001), pp. 4766.##[17] V. Runde, Dual Banach algebras: Connesamenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand., 95 (2004), pp. 124144.##[18] V. Runde, Lectures on amenability, Lecture Notes in Mathematics 1774, Springer Verlag, Berlin, 2002.##]
1

Convergence of an Iterative Scheme for Multifunctions on Fuzzy Metric Spaces
https://scma.maragheh.ac.ir/article_35070.html
10.22130/scma.2018.72350.288
1
Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzukitype multifunctions. The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach contraction principle is that it also gives the convergence of an iterative scheme to a unique fixed point. In this paper, we consider $(X, M, *)$ to be fuzzy metric spaces in Park's sense and we show our results for fixed points of contractive and nonexpansive multifunctions on Hausdorff fuzzy metric space.
0

91
106


Mohammad Esmael
Samei
Department of Mathematics, Faculty of Science, BuAli Sina University, 6517838695, Hamedan, Iran.
Iran
me_samei@yahoo.com
Inexact iterative
Fixed point
Contraction multifunction
Hausdorff fuzzy metric
[[1] R.P. Agarwal, M.A. ElGebeily, and D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Analysis, 87 (2008), pp. 109116.##[2] I. Altun and G. Durmaz, Some fixed point results in cone metric spaces, Rend Circ. Math. Palermo, 58 (2009), pp. 319325.##[3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1922), pp. 133181.##[4] V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Analysis, 74 (2011), pp. 73477355.##[5] J. Caristi, Fixed point theorems for mapping satisfying inwardness conditions, Trans. Amer. Math. Soc., 215 (1976), pp. 241251.##[6] C. Di Bari and C. Vetro, A fixed point theorem for a family of mappings in a fuzzy metric space, Rend Circ. Math. Palermo, 52 (2003), pp. 315321.##[7] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), pp. 395399.##[8] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), pp. 385389.##[9] V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), pp. 245252.##[10] T.L. Hicks, Fixed point theorems for quasimetric spaces, Math. Japon. 33 (1988), pp. 231236.##[11] H. Karayilan and M. Telci, Common fixed point theorem for contractive type mappings in fuzzy metric spaces, Rend. Circ. Mat. Palermo., 60 (2011), pp. 145152.##[12] O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), pp. 326334.##[13] M. Lessonde, Fixed point of Kakutani factorizable multifunctions, J. Math. Anal. Appl., 152 (1990), pp. 4660.##[14] K. Menger, Statistical metrices, Proc. Natl. Acad. Sci., 28 (1942), pp. 535537.##[15] D. Mihet, A banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, 144 (2004), pp. 431439.##[16] J.H. Park, Intiutionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004), pp. 10391046.##[17] J.S. Park, Y.C. Kwun, and J.H. Park, A fixed point theorem in the intiutionistic fuzzy metric spaces, Far East J. Math. Sci. 16 (2005), pp. 137149.##[18] M. Rafi and M.S.M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces, Iranian J. of Fuzzy Systems, 3 (2006), pp. 2329.##[19] D. Reem, S. Reich, and A. Zaslavski, Two results in metric fixed point theory, J. Fixed Point Theory Appl. 1 (2007), pp. 149157.##[20] Sh. Rezapour and P. Amiri, Some fixed point results for multivalued operators in generalized metric spaces, Computers and Mathematics with Applications 61 (2011), pp. 26612666.##[21] Sh. Rezapour and R. Hamlbarani, Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Analysis Appl. 345 (2008), pp. 719724.##[22] J. RodriguesLopez and S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems, 147 (2004), pp. 273283.##[23] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), pp. 18611869.##[24] P. Veeramani, Best approximation in fuzzy metric spaces, J. Fuzzy Math., 9 (2001), pp. 7580.##[25] L.A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), pp. 338353.##]
1

Bounded Approximate Character Amenability of Banach Algebras
https://scma.maragheh.ac.ir/article_35435.html
10.22130/scma.2018.79315.372
1
The bounded approximate version of $varphi$amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded approximate character amenability of some Banach algebras related to locally compact groups are investigated.
0

107
118


Hasan
Pourmahmood Aghababa
Department of Mathematics, University of Tabriz, Tabriz, Iran.
Iran
hpaghababa@tabrizu.ac.ir


Fourogh
Khedri
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
Iran
f.khedri@azaruniv.edu


Mohammad Hossein
Sattari
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
Iran
sattari@azaruniv.ac.ir
Banach algebras
Bounded approximate character amenability
Bounded approximate character contractibility
Locally compact groups
[[1] H.P. Aghababa, L.Y. Shi, and Y.J. Wu, Generalized notions of character amenability, Acta Math. Sin. (Engl. Ser.), 29 (2013), pp. 13291350.##[2] Y. Choi, F. Ghahramani, and Y. Zhang, Approximate and pseudoamenability of various classes of Banach algebras, J. Funct. Anal., 256 (2009), pp. 31583191.##[3] B. Dorofaeff, The Fourier algebra of SL(2, R)?R^n, n≥2, has no multiplier bounded approximate unit, Math. Ann., 297 (1993), pp. 707724.##[4] F. Ghahramani and R.J. Loy, Generalized notions of amenability, J. Funct. Anal., 208 (2004), pp. 229260.##[5] F. Ghahramani, R.J. Loy, and Y. Zhang, Generalized notions of amenability II, J. Funct. Anal., 254 (2008), pp. 17761810.##[6] F. Ghahramani and C.J. Read, Approximate identities in approximate amenability, J. Funct. Anal., 262 (2012), pp. 39293945.##[7] U. Haagerup, An example of a nonnuclear $C^*$algebra, which has the metric approximation property, Invent. math., 50 (1978/79), pp. 279293.##[8] C. Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble), 23 (1973), pp. 91123.##[9] Z. Hu, M.S. Monfared, and T. Traynor, On character amenable Banach algebras, Studia Math., 193 (2009), pp. 5378.##[10] B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972), pp. 196.##[11] E. Kaniuth, A.T. Lau, and J. Pym, On character amenability of Banach algebras, J. Math. Anal. Appl., 344 (2008), pp. 942955.##[12] M.S. Monfared, Character amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc., 144 (2008), pp. 697706.##]
1

Generalized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces
https://scma.maragheh.ac.ir/article_35724.html
10.22130/scma.2018.78754.365
1
Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)leftf^{(n)}(z)right<infty.$ Endowed with the norm begin{align*}leftf right_{mathcal{W}_mu ^{(n)}}=sum_{j=0}^{n1}leftf^{(j)}(0)right+sup_{zin mathbb{D}}mu(z)leftf^{(n)}(z)right,end{align*}the $n$'th weighted type space is a Banach space. In this paper, we characterize the boundedness of generalized weighted composition operators $mathcal{D}_{varphi ,u}^m$ from logarithmic Bloch type spaces $mathcal{B}_{{{log }^beta }}^alpha $ to $n$'th weighted type spaces $ mathcal{W}_mu ^{(n)} $, where $u$ and $varphi$ are analytic functions on $mathbb{D}$ and $varphi(mathbb{D})subseteqmathbb{D}$. We also provide an estimation for the essential norm of these operators.
0

119
133


Kobra
Esmaeili
Faculty of Engineering, Ardakan University, P.O. Box 184, Ardakan, Iran.
Iran
esmaeili@ardakan.ac.ir
Essential norms
Generalized weighted composition operators
Logarithmic Bloch type spaces
$N$th weighted type spaces
[[1] K. Attele, Toeplitz and Hankel operators on Bergman one space, Hokkaido Math. J., 21 (1992), pp. 279293.##[2] K.D. Bierstedt, J. Bonet, and J. Taskinen, Associated weights and spaces of holomorphic functions, Stud. Math., 127 (1998), pp. 137168.##[3] J. Bonet, P. Domanski, and M. Lindstrom, Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions, Canad. Math. Bull., 42 (1999), pp. 139148.##[4] L. Brown and A.L. Shields, Multipliers and cyclic vectors in the Bloch space, Michigan Math. J., 38 (1991), pp. 141146.##[5] K. Esmaeili and M. Lindstrom, Weighted composition operators between Zygmund type spaces and their essential norms, Integr. Equ. Oper. Theory, 75 (2013), pp. 473490.##[6] O. Hyvarinen, M. Kemppainen, M. Lindstrom, A. Rautio, and E. Saukko, The essential norms of weighted composition operators on weighted Banach spaces of analytic function, Integr. Equ. Oper. Theory, 72 (2012), pp. 151157.##[7] B. MacCluer and R. Zhao, Essential norms of weighted composition operators between Blochtype spaces, Rocky Mount. J. Math., 33 (2003), pp. 14371458.##[8] A. MontesRodriguez, Weighted composition operators on weighted Banach spaces of analytic functions, J. London Math. Soc. (3), 61 (2000), pp. 872884.##[9] S. Ohno, K. Stroethoff, and R. Zhao, Weighted composition operators between Blochtype spaces, Rocky Mount. J. Math., 33 (2003), pp. 191215.##[10] H. Qu, Y. Liu, and S. Cheng, Weighted differentiation composition operator from logarithmic Bloch spaces to Zygmundtype spaces, Abstr. Appl. Anal., 2014, Art. ID 832713, 14 pp.##[11] J.C. RamosFernandez, Logarithmic Bloch spaces and their weighted composition operators, Rend. Circ. Mat. Palermo (2), 65 (2016), pp. 159174.##[12] S. Stevic, On new Blochtype spaces, Appl. Math. Comput., 215 (2009), pp. 841849.##[13] S. Stevic, Weighted differentiation composition operators from H∞ and Bloch spaces to nth weightedtype spaces on the unit disk, Appl. Math. Comput., 216 (2010), pp. 36343641.##[14] S. Stevic and A.K. Sharma, Iterated differentiation followed by composition from Blochtype spaces to weighted BMOA spaces, Appl. Math. Comput., 218 (2011), pp. 35743580.##[15] M. Tjani, Compact composition operators on some Mobius invariant Banach spaces [Ph.D. thesis], Michigan State University, 1996.##[16] R. Yoneda, The composition operators on weighted Bloch space, Arch. Math. (Basel), 78 (2002), pp. 310317.##[17] K. Zhu, Bloch type spaces of analytic functions, Rocky Mount. J. Math., 23 (1993), pp. 11431177.##[18] X. Zhu, Generalized weighted composition operators from Bers type spaces into Blochtype spaces, Math. Inequal. Appl., 17 (2014), pp. 187195.##[19] X. Zhu, Products of differentiation, composition and multiplication from Bergman type spaces to bers type space, Integ. Tran. Spec. Funct., 18 (2007), pp. 223231.##]
1

Approximate Duals of $g$frames and Fusion Frames in Hilbert $C^ast$modules
https://scma.maragheh.ac.ir/article_35726.html
10.22130/scma.2018.81624.396
1
In this paper, we study approximate duals of $g$frames and fusion frames in Hilbert $C^ast$modules. We get some relations between approximate duals of $g$frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q$approximate duality of $g$frames and fusion frames to Hilbert $C^ast$modules, where $Q$ is an adjointable operator, and obtain some properties of this kind of approximate duals.
0

135
146


Morteza
Mirzaee Azandaryani
Department of Mathematics, University of Qom, Qom, Iran.
Iran
morteza_ma62@yahoo.com
Frame
$g$frame
Fusion frame
Biorthogonal sequence
Approximate duality
[[1] L. Arambasic, On frames for countably generated Hilbert $C^ast$modules, Proc. Amer. Math. Soc., 135 (2007), pp. 469478.##[2] P. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math. Amer. Math. Soc., 345 (2004), pp. 87113.##[3] O. Christensen and R.S. Laugesen, Approximate dual frames in Hilbert spaces and applications to Gabor frames, Sampl Theory Signal Image Process., 9 (2011), pp. 7790.##[4] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 12711283.##[5] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341366.##[6] M. Frank and D. Larson, Frames in Hilbert $C^ast$modules and $C^ast$algebras, J. Operator Theory., 48 (2002), pp. 273314.##[7] D. Han, W. Jing, D. Larson, and R. Mohapatra, Riesz bases and their dual modular frames in Hilbert $C^ast$modules, J. Math. Anal. Appl., 343 (2008), pp. 246256.##[8] S.B. Heineken, P.M. Morillas, A.M. Benavente, and M.I. Zakowicz, Dual fusion frames, Arch. Math., 103 (2014), pp. 355365.##[9] A. Khosravi and B. Khosravi, Fusion frames and $g$frames in Hilbert $C^ast$modules, Int. J. Wavelets Multiresolut. Inf. Process., 6 (2008), pp. 433446.##[10] A. Khosravi and B. Khosravi, Gframes and modular Riesz bases, Int. J. Wavelets Multiresolut. Inf. Process., 10 (2012), pp. 112.##[11] A. Khosravi and M. Mirzaee Azandaryani, Approximate duality of $g$frames in Hilbert spaces, Acta. Math. Sci., 34 (2014), pp. 639652.##[12] E.C. Lance, Hilbert $C^ast$modules: A Toolkit for Operator Algebraists, Cambridge University Press, Cambridge., 1995.##[13] M. Mirzaee Azandaryani, Approximate duals and nearly Parseval frames, Turk. J. Math., 39 (2015), pp. 515526.##[14] M. Mirzaee Azandaryani, Bessel multipliers and approximate duals in Hilbert $C^astmodules$, J. Korean Math. Soc., 54 (2017), pp. 10631079.##[15] M. Mirzaee Azandaryani, On the approximate duality of $g$frames and fusion frames, U. P. B. Sci. Bull. Ser A., 79 (2017), pp. 8393.##[16] W. Sun, Gframes and gRiesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437452.##[17] X. Xiao and X. Zeng, Some properties of $g$frames in Hilbert $C^ast$modules, J. Math. Anal. Appl., 363 (2010), pp. 399408.##]
1

Primitive Ideal Space of Ultragraph $C^*$algebras
https://scma.maragheh.ac.ir/article_35729.html
10.22130/scma.2018.82725.404
1
In this paper, we describe the primitive ideal space of the $C^*$algebra $C^*(mathcal G)$ associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $ C^* $algebra $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gaugeinvariant primitive ideals. Our results generalize the Hong and Szyma$ acute{ mathrm { n } } $ski's description of the primitive ideal space of a graph $ C ^ * $algebra by a simpler method.
0

147
158


Mostafa
Imanfar
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.
Iran
m.imanfar@aut.ac.ir


Abdolrasoul
Pourabbas
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.
Iran
arpabbas@aut.ac.ir


Hossein
Larki
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Iran.
Iran
h.larki@scu.ac.ir
Ultragraph
Ultragraph $C^*$algebra
Primitive ideal
[[1] G. Abrams, P. Ara, and M. Siles Molina, Leavitt Path Algebras, Lecture Notes in Mathematics Vol. 2191, Springer, London, 2017.##[2] T. Bates, D. Pask, I. Raeburn, and W. Szymanski, The $C^*$algebras of rowfinite graphs, New York J. Math., 6 (2000), pp. 307324.##[3] T.M. Carlsen, S. Kang, J. Shotwell, and A. Sims, The primitive ideals of the CuntzKrieger algebra of a rowfinite higherrank graph with no sources, J. Funct. Anal., 266 (2014), pp. 25702589.##[4] T.M. Carlsen and A. Sims, On Hong and Szymanski's description of the primitiveideal space of a graph algebra, Operator algebras and applicationsthe Abel Symposium (2015), Abel Symp., 12, Springer, [Cham], (2017), pp. 115132.##[5] J. Cuntz and W. Krieger, A class of $C^*$algebras and topological Markov chains, Invent. Math., 56 (1980), pp. 251268.##[6] R. Exel and M. Laca, CuntzKrieger algebras for infinite matrices, J. Reine Angew. Math., 512 (1999), pp. 119172.##[7] N. Fowler, M. Laca, and I. Raeburn, The $C^*$algebras of infinite graphs, Proc. Amer. Math. Soc., 128 (2000), pp. 23192327.##[8] J. Hong and W. Szymanski, The primitive ideal space of the $C^*$algebras of infinite graphs, J. Math. Soc. Japan, 56 (2004), pp. 4564.##[9] T. Katsura, P.S. Muhly, A. Sims, and M. Tomforde, Utragraph $C^*$algebras via topological quivers, Studia Math., 187 (2008), pp. 137155.##[10] A. Kumjian, D. Pask, and I. Raeburn, CuntzKrieger algebras of directed graphs, Pacific J. Math., 184 (1998), pp. 161174.##[11] H. Larki, Primitive ideals and pure infiniteness of ultragraph $C^*$algebras, J. Korean Math. Soc., 56 (2019), pp. 123.##[12] H. Larki, Primitive ideal space of higherrank graph $C^*$algebras and decomposability, J. Math. Anal. Appl., 469 (2019), pp. 7694.##[13] M. Tomforde, A unified approach to ExelLaca algebras and $C^*$algebras associated to graphs, J. Operator Theory, 50 (2003), pp. 345368.##]
1

Proximity Point Properties for Admitting Center Maps
https://scma.maragheh.ac.ir/article_35727.html
10.22130/scma.2018.79127.368
1
In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we show that in some conditions, the set of all best proximity points is nonempty and compact.
0

159
167


Mohammad Hosein
Labbaf Ghasemi
Department of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 8818634141, Iran.
Iran
mhlgh@yahoo.com


Mohammad Reza
Haddadi
Faculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.
Iran
haddadi@abru.ac.ir


Noha
Eftekhari
Department of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 8818634141, Iran.
Iran
eftekharinoha@yahoo.com
Admitting center map
Nonexpansive map
Cochebyshev set
Best proximity pair
[[1] A. Abkar and M. Gabeleh, Best proximity points of nonself mappings, Top, 21 (2013), pp. 287295.##[2] R.P. Agarwal, E. Karapınar, D. O'Regan, and A.F. RoldánLópezdeHierro, Fixed point theory in metric type spaces, Switzerland, Springer, 2015.##[3] R.P. Agarwal, D. O'Regan, and D.R. Sahu, Fixed point theory for Lipschitziantype mappings with applications, New York, Springer, 2009.##[4] T.D. Benavides, J.G. Falset, E. LlorensFuster, and P.L. Ramírez, Fixed point properties and proximinality in Banach spaces, Nonlinear Anal., 71 (2009), pp. 15621571.##[5] X.P. Ding and K.K. Tan, On equilibria of noncompact generalized games, J. Math. Anal. Appl., 177 (1993), pp. 226238.##[6] W.G. Dotson, On the Mann iterative process, Trans. Amer. Math. Soc., 149 (1970), pp. 6573.##[7] A.A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), pp. 10011006.##[8] J. GarciaFalset, E. LlorensFuster, and S. Prus, The fixed point property for mappings admitting a center, Nonlinear Anal., 66 (2007), pp. 12571274.##[9] M.R. Haddadi and S.M. Moshtaghioun, Some results on the best proximity pair, Abstract and Applied Analysism, 2011 (2011).##[10] W.K. Kim and S. Kum, Best proximity pairs and Nash equilibrium pairs, J. Korean Math. Soc., 45 (2008), pp. 12971310.##[11] W. Kirk and N. Shahzad, Fixed point theory in distance spaces, Springer, 2016.##[12] T.D. Narang, On best coapproximation in normed linear spaces, Rocky Mountain J. Math., 1 (1992), pp. 265287.##[13] H.K. Nashine, P. Kumam, and C. Vetro, Best proximity point theorems for rational proximal contractions, Fixed Point Theory Appl., 2013 (2013), pp. 211.##[14] V.S. Raj, A best proximity point theorem for weakly contractive nonselfmappings, Nonlinear Anal., 74 (2011), pp. 48044808.##[15] J. Zhang, Y. Su, and Q. Cheng, Best proximity point theorems for generalized contractions in partially ordered metric spaces, Fixed Point Theory Appl., 2013 (2013), pp. 17.##]
1

Some Properties of Continuous $K$frames in Hilbert Spaces
https://scma.maragheh.ac.ir/article_35964.html
10.22130/scma.2018.85866.432
1
The theory of continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory. The $K$frames were introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of $K$frames, there are many differences between $K$frames and standard frames. $K$frames, which are a generalization of frames, allow us in a stable way, to reconstruct elements from the range of a bounded linear operator in a Hilbert space. In this paper, we get some new results on the continuous $K$frames or briefly c$K$frames, namely some operators preserving and some identities for c$K$frames. Also, the stability of these frames are discussed.
0

169
187


Gholamreza
Rahimlou
Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.
Iran
grahimlou@gmail.com


Reza
Ahmadi
Institute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.
Iran
rahmadi@tabrizu.ac.ir


Mohammad Ali
Jafarizadeh
Faculty of Physic, University of Tabriz,
Tabriz, Iran.
Iran
jafarizadeh@tabrizu.ac.ir


Susan
Nami
Faculty of Physic, University of Tabriz,
Tabriz, Iran.
Iran
s.nami@tabrizu.ac.ir
$K$frame
cframe
c$K$frame
Local c$K$atoms
[[1] S.T. Ali, J.P. Antoine, and J.P. Gazeau, Continuous frames in Hilbert spaces, Ann.Phys., 222 (1993), pp. 137.##[2] H. Bolcskel, F. Hlawatsch, and H.G. Feichyinger, FrameTheoretic analysis of oversampled filter bank, IEEE Trans. Signal Processing., 46 (1998), pp. 3256 3268.##[3] P.G. Casazza, G. Kutyniok, and S. Li, Fusion frames and Distributed Processing, Appl. Comput. Harmon. Anal., 25 (2008), pp. 114132.##[4] O. Christensen, Introduction to frames and Riesz bases, Birkhasuser, Boston, 2003.##[5] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal Expansions, J. Math. Phys., 27 (1986), pp. 12711283.##[6] R.G. Douglas, On majorization, Factorization and range inclusion of operators on Hilbert spaces, Proc. Amer. Math. Soc., 17 (1966), pp. 413415.##[7] R.J. Duffin and A.C. Schaeffer, A class of nonharmonik Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341366.##[8] M.H. Faroughi and E. Osgooei, CFrames and CBessel Mappings, Bull. Iran. Math., 38 (2012), pp. 203222.##[9] L. Gu avruc ta, Frames for operators, Appl. Comput. Harmon. Anal., 32 (2012), pp. 139144.##[10] G. Kaiser, A Friendly Guide to Wavelets, Birkhauser, Boston, 1994.##[11] A. Rahimi, A. Najati, and Y.N. Dehgan, Continuous frame in Hilbert space, Methods of Functional Analysis and Topology., 12 (2006), pp. 170182.##[12] GH. Rahimlou, R. Ahmadi, M.A. Jafarizadeh, and S. Nami, Continuous $k$Frames and their duals, (2018) Submitted.##[13] W. Rudin, Real and Complex Analysis, New York, Tata Mc GrawHill Editions, 1987.##[14] X. Xiao, Y. Zhu, and L. Gu avruc ta, Some Properties of $K$frames in Hilbert Spaces, Results. Math., 63 (2012), pp. 12431255.##]
1

A Proposed Preference Index For Ranking Fuzzy Numbers Based On $alpha$Optimistic Values
https://scma.maragheh.ac.ir/article_35734.html
10.22130/scma.2018.73477.303
1
In this paper, we propose a novel method for ranking a set of fuzzy numbers. In this method a preference index is proposed based on $alpha$optimistic values of a fuzzy number. We propose a new ranking method by adopting a level of credit in the ordering procedure. Then, we investigate some desirable properties of the proposed ranking method.
0

189
201


Mehdi
Shams
Department of Statistics, School of Mathematics, University of Kashan, Kashan,Iran.
Iran
mehdi_shams1357@yahoo.com


Gholamreza
Hesamian
Department of Mathematical Sciences, Payame Noor University, Tehran, Iran.
Iran
ghesamian@math.iut.ac.ir
$alpha$Optimistic value
Fuzzy ranking
Preference index
Roboustness
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1

Topological Centers and Factorization of Certain Module Actions
https://scma.maragheh.ac.ir/article_35723.html
10.22130/scma.2018.76242.344
1
Let $A$ be a Banach algebra and $X$ be a Banach $A$bimodule with the left and right module actions $pi_ell: Atimes Xrightarrow X$ and $pi_r: Xtimes Arightarrow X$, respectively. In this paper, we study the topological centers of the left module action $pi_{ell_n}: Atimes X^{(n)}rightarrow X^{(n)}$ and the right module action $pi_{r_n}:X^{(n)}times Arightarrow X^{(n)}$, which inherit from the module actions $pi_ell$ and $pi_r$, and also the topological centers of their adjoints, from the factorization property point of view, and then, we investigate conditions under which these bilinear maps are Arens regular or strongly Arens irregular.
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Sedigheh
Barootkoob
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.
Iran
s.barutkub@ub.ac.ir
Topological centers
Module actions
Arens regular
Strongly Arens irregular
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