2018
11
1
0
143
Coherent Frames
2
2
Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of a single element of Hilbert space $mathcal{H}$ under some unitary representation $pi$ of $G$ on $mathcal{H}$. It is interesting that most of important frames are coherent. We investigate canonical dual and combinations of this frames
1

1
11


Ataollah
Askari Hemmat
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169133, Kerman, Iran.
Department of Mathematics, Faculty of Mathematics
Iran
askari@mail.uk.ac.ir


Ahmad
Safapour
Department of Mathematics, Faculty of Mathematical Sciences, ValieAsr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
Department of Mathematics, Faculty of Mathematical
Iran
safapour@vru.ac.ir


Zohreh
Yazdani Fard
Department of Mathematics, Faculty of Mathematical Sciences, ValieAsr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.
Department of Mathematics, Faculty of Mathematical
Iran
zohreh.yazdanifard@gmail.com
Coherent frame
Continuous frame
Locally compact group
Unitary representation
[[1] S.T. Ali, J.P. Antoine, and J.P. Gazeau, Continuous frames in Hilbert spaces, Ann. Phys., 222 (1993), pp. 137.##[2] J.P. Antoine and P. Vandergheynst, Wavelets on 2Sphere: a Group Theoretical Approach, Appl. Comput. Harmon. Anal., 7 (1999), pp. 130.##[3] M. Azhini and M. Beheshti, Some results on continuous frames for Hilbert Spaces, Int. J. Industrial Mathematics, 2 (2001), pp. 3742.##[4] P. Balazs and P.D.T. Stoven, Representation of the inverse of a frame multiplier, J. Math. Anal. Appl., 422 (2015), pp. 981994.##[5] H. Bölcskel, F. Hlawatsch, and H.G. Feichtinger, Frametheoretic analysis of oversampled filter banks, IEEE Trans. Signal Process., 46 (1998), pp. 32563268.##[6] E.J. Candès and D. Donoho, New tight frames of curvelets and optimal representations of objects with piecewise $C^2$ singularities, Comm. Pure and Appl. Math., 56 (2004), pp. 216266.##[7] P.G. Casazza and G. Kutyniok, Finite Frames: Theory and Applications, Birkhäuser, Boston, 2012.##[8] O. Chritensen, An Introduction to Frames and Riesz Bases, Birkhäuser, Boston, 2002.##[9] I. Daubechies, A. Grasmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 12711283.##[10] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341366.##[11] G.B. Folland, A Course in abstract harmonic analysis, CRC Press, Florida, 1995.##[12] D. Gabor, Theory of communication, J. Inst. Electr. Eng. London, 93 (1946), pp. 429457.## [13] K. Grächening, The homogeneous approximation property and the comparison theorem for coherent frames, sampl. Theory Signal Image Process., 7 (2008), pp. 271279.##[14] D. Han and D.R. Larson, Frames, Bases, and Group Representations, Mem. Amer. Math. Soc., 147 (2000), pp. 194.##[15] R.W. Heath and A.J. Paulraj, Linear dispersion codes for MIMO systems based on frame theory, IEEE Trans. Signal Process., 50 (2002), pp. 24292441.##[16] G. Kaiser, A Friendly Guide to Wavelets, Birkhäuser, Boston, 1994.##[17] R.V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras, Vol. I, Academic Press, New York, 1983.##[18] A. Rahimi, A. Najati, and Y.N. Dehghan, Continuous frames in Hilbert spaces, Meth. Func. Anal. Top., 12 (2006), pp. 170182.##]
On Polar Cones and Differentiability in Reflexive Banach Spaces
2
2
Let $X$ be a Banach space, $Csubset X$ be a closed convex set included in a wellbased cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set $C$, so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqemptyset$. The latter is a primary condition for subdifferentiability of the support function $sigma_C$. Eventually, we study Gateaux differentiability of support function $sigma_C$ on two sets, the polar cone of $K$ and ${mathop{rm int}}(mathrm{dom} sigma_C)$.
1

13
23


Ildar
Sadeqi
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
Department of Mathematics, Faculty of Science,
Iran
esadeqi@sut.ac.ir


Sima
Hassankhali
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
Department of Mathematics, Faculty of Science,
Iran
shassankhali@sut.ac.ir
Recession cone
Polar cone
Bounded base
Support function
Gateaux differentiability
[[1] C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd Edition, SpringerVerlag, Berlin, 2006.##[2] J.M. Borwein and J.D. Vanderwerff, Convex functions: constructions, characterizations and counterexamples, Encyclopedia of Mathematics and its Applications, 109. Cambridge. Univ. Press, Cambridge, 2010. ##[3] E. Casini and E. Miglierina, Cones with bounded and unbounded bases and reflexivity, Nonlinear Anal., 72 (2010), pp. 23562366.##[4] M. Fabian, P. Habala, P. Hajek, V. Montesinos, and V. Zizler, Banach space theory, the basis for linear and unlinear analysis, CMS Books in Math, Springer, Canada, 2011.##[5] Z.Q . Han, Relationship between solid cones and cones with bases, Optim. Theory Appl., 90 (1996), pp. 457463.##[6] Z.Q. Han, Remarks on the angle poperty and solid cones, J. Optim. Theory Appl. 82 (1994), pp. 149157.##[7] G. Isac, Pareto optimization in infinitedimensional spaces, the importance of nuclear cones, J. Math. Anal. Appl., 182 (1994), pp. 393404.##[8] J. Jahn, Vector optimization theorem, theory, application and existence, Springer, Verlag Berlin Heidelberg, 2011.##[9] A. Khan, Ch. Christiane, and C. Zalinescu, Setvalued Optimization, An introduction with application, Springer, Verlag Berlin Heidelberg, 2015.##[10] I.A . Polyrakis, Demand functions and reflexivity, J. Math. Anal. Appl., 338 (2008), pp. 695704.##[11] J.H. Qiu, On Solidness of Polar Cones, J. Optim. Theory Appl., 109 (2001), pp. 199–214.##]
MeirKeeler Type Contraction Mappings in $c_0$triangular Fuzzy Metric Spaces
2
2
Proving fixed point theorem in a fuzzy metric space is not possible for MeirKeeler contractive mapping. For this, we introduce the notion of $c_0$triangular fuzzy metric space. This new space allows us to prove some fixed point theorems for MeirKeeler contractive mapping. As some pattern we introduce the class of $alphaDelta$MeirKeeler contractive and we establish some results of fixed point for such a mapping in the setting of $c_0$triangular fuzzy metric space. An example is furnished to demonstrate the validity of these obtained results.
1

25
41


Masoomeh
Hezarjaribi
Department of Mathematics, Payame Noor University, p.o.box.193953697, Tehran, Iran.
Department of Mathematics, Payame Noor University,
Iran
hezarjaribimasoomeh@gmail.com
$c_0$triangular fuzzy metric space
$alphaDelta$MeirKeeler contractive
Fixed point
[[1] C. Di Bari and C. Vetro, A fixed point theorem for a family of mappings in a fuzzy metric space, Rend. Circ. Mat. Palermo, 52 (2003), pp. 315321.##[2] C. Di Bari and C. Vetro, Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math., 13 (2005), pp. 973982.##[3] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), pp. 395399.##[4] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), pp. 385389.##[5] J. Jachymski, Equivalent condition and the MeirKeeler type theorems , J. Math. Anal. Appl., 194 (1995), pp. 293303.##[6] E. Karapinar, P. Kumam, and P. Salimi, On $alpha$$psi$MeirKeeler contractive mappings, Fixed Point Theory Appl., 1 (2013), pp. 112.##[7] I. Kramosil and J. Michálek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), pp. 336344.##[8] A. Meir and E. Keeler, A theorem on contraction mapping, J. Math. Anal. Appl., 28 (1969), pp. 326329.##[9] S. Park and B.E. Rhoades, MeirKeeler type contractive condition, Math. Japon., 26 (1981), pp. 1320.##[10] A.C.M. Ran and M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), pp. 14351443.##[11] B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for $alpha$$psi$contractive type mappings, Nonlinear Anal., 75 (2012), pp. 21542165.##[12] Y.Shen, D.Qiu, and W.Chenc, Fixed point theorems in fuzzy metric spaces, Appl. Math. Letters, 25 (2012), pp. 138141.##[13] L.A. Zadeh, Fuzzy sets, Information & Control, 8 (1965), pp. 338353.##]
On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions
2
2
In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.
1

43
63


Sanjib
Kumar Datta
Department of Mathematics, University of Kalyani, P.O.Kalyani, DistNadia, PIN741235, West Bengal, India.
Department of Mathematics, University of
Iran
sanjib_kr_datta@yahoo.co.in


Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.Krishnagar, DistNadia, PIN741101, West Bengal, India.
Rajbari, Rabindrapalli, R. N. Tagore Road,
Iran
tanmaybiswas_math@rediffmail.com
Entire function
Generalized relative order
Generalized relative lower order
Generalized relative type
Generalized relative weak type
[[1] L. Bernal, Crecimiento relativo de funciones enteras. Contribucion al estudio de lasfunciones enteras conindice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.##[2] L. Bernal, Orden relative de crecimiento de funciones enteras, Collect. Math., Vol. 39 (1988), pp. 209229.##[3] S.K. Datta and T. Biswas, Growth of entire functions based on relative order, Int. J. Pure Appl. Math., Vol. 51, No. 1 (2009), pp. 4958.##[4] S.K. Datta and A. Biswas, On relative type of entire and meromorphic functions, Advances in Applied Mathematical Analysis, Vol. 8, No. 2 (2013), pp. 6375.##[5] S.K. Datta and T. Biswas, Relative order of composite entire functions and some related growth properties, Bull. Cal. Math. Soc., Vol. 102, No.3 (2010) pp.259266.##[6] S.K. Datta, T. Biswas and R. Biswas, Comparative growth properties of composite entire functions in the light of their relative order, The Mathematics Student, Vol. 82, No. 14 (2013), pp. 18.##[7] S.K. Datta, T. Biswas, and R. Biswas, On relative order based growth estimates of entire functions, International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 7, No. II (March, 2013), pp. 5967.##[8] S.K. Datta, T. Biswas, and D.C. Pramanik, On relative order and maximum term related comparative growth rates of entire functions, Journal of Tripura Mathematical Society, Vol. 14 (2012), pp. 6068.##[9] S.K. Datta, T. Biswas, and C. Ghosh, Growth analysis of entire functions concerning generalized relative type and generalized relative weak type, Facta Universitatis (NIS) Ser. Math. Inform, Vol. 30, No. 3 (2015), pp. 295324.##[10] S.K. Datta and A. Jha, On the weak type of meromorphic functions, Int. Math. Forum, Vol. 4, No. 12(2009), pp. 569579.##[11] B.K. Lahiri and D. Banerjee, Generalised relative order of entire functions, Proc. Nat. Acad. Sci. India, Vol. 72(A), No. IV (2002), pp. 351271.##[12] C. Roy, Some properties of entire functions in one and several complex variables, Ph.D. Thesis, submitted to University of Calcutta, 2009.##[13] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., Vol. 69 (1963), pp. 411414.##[14] E.C. Titchmarsh, The theory of functions, 2nd ed. Oxford University Press, Oxford, (1968).##[15] G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, (1949).##]
$G$dual Frames in Hilbert $C^{*}$module Spaces
2
2
In this paper, we introduce the concept of $g$dual frames for Hilbert $C^{*}$modules, and then the properties and stability results of $g$dual frames are given. A characterization of $g$dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$dual frames for Riesz bases in Hilbert spaces is not satisfied in general Hilbert $C^*$modules.
1

65
79


Fatemeh
Ghobadzadeh
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
Department of Mathematics and Applications,
Iran
gobadzadehf@yahoo.com


Abbas
Najati
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
Department of Mathematics and Applications,
Iran
a.nejati@yahoo.com
Frame
$g$dual frame
Hilbert $C^{*}$module
[[1] P. Balazs and D.T. Stoeva, Representation of the inverse of a frame multiplier, J. Math. Anal. Appl., 422 (2015), pp. 981994.##[2] O. Christensen and R.S. Laugesen, Approximately dual frame pairs in Hilbert spaces and applications to Gabor frames, Sampl. Theory Signal Image Process. 9 (2010), pp. 7789.##[3] M.A. Dehghan and M.A. Hasankhani Fard, $G$dual frames in Hilbert spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 75 (2013), pp. 129140.##[4] L. Dengfeng and L. Yanting, $G$dual frames for generalized frames, Adv. Math., (China), 45 (2016), pp. 919931.##[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.R. Larson, Frames in Hilbert $C^*$modules and $C^*$algebras, J. Operator Theory, 48 (2002), pp. 273314.##[7] M. Frank and D.R. Larson, A module frame concept for Hilbert $C^*$modules, The functional and harmonic analysis of wavelets and frames (San Antonio, TX, 1999), 207233, Contemp. Math., 247, Amer. Math. Soc., Providence, RI, 1999.##[8] F. Ghobadzadeh, A. Najati, G.A. Anastassiou, and C. Park, Woven frames in Hilbert $C^*$module spaces, J. Comput. Anal. Appl., 25 (2018), pp. 12201232.##[9] F. Ghobadzadeh, A. Najati, and E. Osgooei, Modular frames and invertibility of multipliers in Hilbert $C^*$modules, (submitted).##[10] D. Han, D. Larson, W. Jing, and R.N. Mohapatra, Riesz bases and their dual modular frames in Hilbert $C^*$modules, J. Math. Anal. Appl., 343 (2008), pp. 246256.##[11] M.A. Hasankhanifard and M.A. Dehghan, $G$dual functionvalued frames in $L^2(0,$∞$)$, Wavel. Linear Algebra, 2 (2015), pp. 3947.##[12] H. Javanshiri, Some properties of approximately dual frames in Hilbert spaces, Results Math., 70 (2016), pp. 475485.##[13] E.C. Lance, Hilbert $C^*$modules  a toolkit for operator algebraists, London Mathematical Society Lecture Note Series, vol. 210. Cambridge University Press, England, 1995.##[14] H. Li, A Hilbert $C^*$module admitting no frames, Bull. London Math. Soc., 42 (2010), pp. 388394.##[15] M. Mirzaee Azandaryani, Approximate duals and nearly Parseval frames, Turkish J. Math., 39 (2015), pp. 515526.##[16] G.J. Murphy, $C^*$algebras and operator theory, Academic Press, San Diego, 1990.##[17] A. Najati, M. Mohammadi Saem, and P. Guavruta, Frames and operators in Hilbert $C^*$modules, Oper. Matrices, 10 (2016), 7381.##[18] M. RashidiKouchi, A. Nazari, and M. Amini, On stability of $g$frames and $g$Riesz bases in Hilbert $C^*$modules, Int. J. Wavelets Multiresolut. Inf. Process., 12 (2014), pp. 116.##[19] M. RashidiKouchi and A. Rahimi, Controlled frames in Hilbert $C^*$modules, Int. J. Wavelets Multiresolut. Inf. Process., 15 (2017), pp. 115.##[20] D.T. Stoeva and P. Balazs, Invertibility of multipliers, Appl. Comput. Harmon. Anal., 33 (2012), pp. 292299.##]
Some Fixed Point Results for the Generalized $F$suzuki Type Contractions in $b$metric Spaces
2
2
Compared with the previous work, the aim of this paper is to introduce the more general concept of the generalized $F$Suzuki type contraction mappings in $b$metric spaces, and to establish some fixed point theorems in the setting of $b$metric spaces. Our main results unify, complement and generalize the previous works in the existing literature.
1

81
89


Sumit
Chandok
School of Mathematics, Thapar University, Patiala147004, India.
School of Mathematics, Thapar University,
Iran
sumit.chandok@thapar.edu


Huaping
Huang
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China.
School of Mathematical Sciences, Beijing
Iran
mathhhp@163.com


Stojan
Radenović
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.
Faculty of Mechanical Engineering, University
Iran
radens@beotel.net
Fixed point
Generalized $F$Suzuki contraction
$b$metric space
[[1] M. Abbas, M. Berzig, T. Nazir, and E. Karapinar, Iterative approximation of fixed points for presic type $F$contraction operators, Uni. Pol. Bucharest Sci. Bul. AAppl. Math. Phy., 78 (2) (2016), pp. 147160.##[2] H.H. Alsulami, E. Karapinar, and H. Piri, Fixed points of generalized FSuzuki type contraction in complete $b$metric spaces, Dis. Dyn. Nat. Soc., Volume 2015, Article ID 969726, 8 pages.##[3] H.H. Alsulami, E. Karapinar, and H. Piri, Fixed points of modified $F$contractive mappings in complete metriclike spaces, J. Funct. Spaces, Volume 2015, Article ID 270971, 9 pages.##[4] I.A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal., 30 (1989), pp. 2637.##[5] L. Ciric, S. Chandok, and M. Abbas, Invariant approximation results of generalized nonlinear contractive mappings, Filomat, 30 (2016), pp. 38753883.##[6] S. Czerwik, Contraction mappings in $b$metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), pp. 511.##[7] H. Ding, M. Imdad, S. Radenovic, and J. Vujakovic, On some fixed point results in $b$metric, rectangular and $b$rectangular metric spaces, Arab J. Math. Sci., 22 (2016), pp. 151164.##[8] N.V. Dung, and V.L. Hang, A fixed point theorem for generalized $F$contractions on complete metric spaces, Vietnam J. Math., 43 (2015), pp. 743753.##[9] M. Jovanovic, Z. Kadelburg, and S. Radenovic, Common fixed point results in metrictype spaces, Fixed Point Theory Appl., Volume 2010, Article ID 978121, 15 pages.##[10] E. Karapinar, M.A. Kutbi, H. Piri, and D. ORegan, Fixed points of conditionally $F$contractions in complete metriclike spaces, Fixed Point Theory Appl., 2015 (2015), Article ID 126, 14 pages.##[11] H. Piri, and P. Kumam, Fixed point theorems for generalized $F$Suzukicontraction mappings in complete $b$metric spaces, Fixed Point Theory Appl., 2016 (2016), Article ID 90, 13 pages.##[12] S. Shukla, S. Radenovic, and Z. Kadelburg, Some fixed point theorems for ordered $F$generalized contractions in 0$f$orbitally complete partial metric spaces, Theory Appl. Math. Comput. Sci., 4 (2014), pp. 8798.##[13] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), Article ID 94, 11 pages.##[14] D. Wardowski, and N.V. Dung, Fixed points of $F$weak contractions on complete metric spaces, Demonstratio Math., 67 (2014), pp. 146155.##]
Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$algebras
2
2
Let $A$ be a unital $C^{*}$algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.
1

91
97


Fatemeh
Golfarshchi
Department of Multimedia, Tabriz
Islamic Art University, Tabriz, Iran.
Department of Multimedia, Tabriz
Islamic
Iran
f.golfarshchi@tabriziau.ac.ir


Ali Asghar
Khalilzadeh
Department of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.
Department of Mathematics, Sahand University
Iran
khalilzadeh@sut.ac.ir
$C^{*}$algebra
Hilbert $C^{*}$module
Invertibility preserving
Spectral radius preserving
Jordan isomorphism
[[1] B. Aupetit, Spectrumpreserving linear mappings between Banach algebras or JordanBanach algebras, J. Lond. Math Soc., 62 (2000) 917924.##[2] B. Blackadar, Theory of $C^{*}$algebras and Von Neumann algebras, SpringerVerlag, New York, 2006.##[3] M. Bresar and P. Semrl, Linear maps preserving the spectral radius, J. Funct. Anal., 142 (1996) 360368.##[4] M. Bresar and P. Semrl, Invertibility preserving maps preserve idempotents, Michigan Math. J., 45 (1998) 483488.##[5] A. Jafarian and A.R. Sourour, Spectrum preserving linear maps, J. Funct. Anal., 66 (1986) 255261.##[7] E.C. Lance, Hilbert $C^{*}$modules A toolkit for operator algebraists, Lond. Math. Soc., Lecture Notes Ser, 210, Cambridge University Press, Cambridge, 1995.##[8] M. Marcus and B.N. Moyls, Linear transformations on algebras of matrices, Canad. J. Math., 11 (1959) 6166.##[9] M. Mathieu and A.R. Sourour, Hereditary properties of spectral isometries, Arch. Math., 82 (2004) 222229.##[10] L. Molnar, Some characterizations of the automorphisms of $B(H)$ and $C(X)$, Proc. Amer. Math. Soc., 130 (2001) 111120.##[11] J. Murphy, $C^{*}$algebras and Operator Theory, Academic Press, Boston, 1990.##[12] S. Sakai, $C^{*}$algebras and $W^{*}$algebras, SpringerVerlag, New York, 1971.##[13] A.R. Sourour, Invertibility preserving linear maps on $L(X)$, Trans. Amer. Math. Soc., {348} (1996) 1330.##[14] N.E. WeggeOlsen, $K$theory and $C^{*}$algebras, Oxford University Press, New York, 1993.##]
A Coupled Random Fixed Point Result With Application in Polish Spaces
2
2
In this paper, we present a new concept of random contraction and prove a coupled random fixed point theorem under this condition which generalizes stochastic Banach contraction principle. Finally, we apply our contraction to obtain a solution of random nonlinear integral equations and we present a numerical example.
1

99
113


Rashwan Ahmed
Rashwan
Department of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt.
Department of Mathematics, Faculty of Science,
Iran
rashwan10@gmail.com


Hasanen AbuelMagd
Hammad
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
Department of Mathematics, Faculty of Science,
Iran
Coupled random fixed point
$varphi $contraction
Polish space
Random nonlinear integral equations
[[1] M. Abbas, M.A. Khan, and S. Radenovic, Common coupled fixed point theorems in cone metric spaces for wcompatible mapping, Appl. Math. Comput., 217 (2010) 195202.##[2] M.U. Ali, T. Kamran, and M. Postolache, Solution of Volterra integral inclusion in bmetric spaces via new fixed point theorem, Nonlin. Anal. Modelling and Control, 22 (2017) 1730.##[3] M.U. Ali and T. Kamran, Multivalued Fcontraction and related fixed point theorems with application, Filomat, 30 (2016), 37793793.##[4] I. Arandjelovic, Z. Radenovic, and S. Radenovic, BoydWongtype common fixed point results in cone metric spaces, Appl. Math Comput., 217, (2011), 71677171.##[5] H. Aydi, M. Postolache, and W.Shatanawi, Coupled fixed point results for (ψ,φ)weakly contractive mappings in ordered Gmetric spaces, Comput. Math. Appl., 63, (2012), 298309.##[6] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3, (1922),133181.##[7] R. Batra and S. Vashistha, Fixed points of an Fcontraction on metric spaces with a graph, Int. J. Comput. Math., 91, (2014), 24832490.##[8] A.T. BharuchaReid, Random Integral equations, Mathematics in Science and Engineering, 96, Academic Press, New York, 1972.##[9] T.G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. Theor., 65, (2006), 13791393.##[10] D.W. Boyd and J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20, (1969), 458464.##[11] J. Caballero, B.B. López, and K. Sadarangani, On monotonic solutions of an integral equation of Volterra type with supremum, J. Math. Anal. Appl., 305, (2005), 304315.##[12] M. Cosentino and P. Vetro, Fixed point results for Fcontractive mappings of HardyRogerstype, Filomat, 28, (2014), 715722.##[13] O. Hans, Reduzierende zufallige transformationen, Czechoslov. Math. J., 7, (1957), 154158.##[14] S. Itoh, Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl., 67, (1979), 261273.##[15] M.C. Joshi and R.K. Bose, Some topics in nonlinear functional analysis, Wiley Eastern Ltd., New Delhi, (1984).##[16] T. Kamran, M. Postolache, M.U. Ali, and Q. Kiran, Feng and Liu type Fcontraction in bmetric spaces with an application to integral equations, J. Math. Anal., 7, (2016), 1827.##[17] V. Lakshmikantham and Lj. Ciric, Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces, Stoch. Anal. and Appl., 27, (2009), 12461259.##[18] A. Spacek, Probability Measure in Infinite Cartesian Products, Czechoslovak Academy of Sciences Pragu, Czechoslovak, 210220, (1959).##[19] H.K. Pathak, M.S. Khan, and R. Tiwari, A common fixed point theorems and its application to nonlinear integral equations, Computer Math. Appl., 53, (2007), 961971.##[20] E. Rakotch, A note in contractive mappings, Proc. Amer. Math. Soc., 13, (1962), 459465.##[21] R.A. Rashwan and D.M. Albaqeri, A common random fixed point theorem and application to random integral equations, Int. J. Appl. Math. Reser., 3, (2014), 7180.##[22] R.A. Rashwan and H.A. Hammad, A coupled random fixed point theorem in quasipartial metric spaces, JP J. Fixed Point Theory Appl., 11, (2016), 161184.##[23] R.A. Rashwan and H.A. Hammad, On random coincidence point and random coupled fixed point theorems in ordered metric spaces, JP J. Fixed Point Theory Appl., 11, (2016), 125160.##[24] R.A. Rashwan and H.A. Hammad, Random common fixed point theorem for random weakly subsequentially continuous generalized contractions with application, Int. J. Pure Appl. Math., 109, (2016), 813826.##[25] R.A. Rashwan and H.A. Hammad, Random fixed point theorems with an application to a random nonlinear integral equation, Journal of Linear and Topological Algebra, 5, (2016), 119133.##[26] A. Spacek, Zufallige Gleichungen, Czechoslovak Math. J., 5, (1955), 462466.##[27] E. Tarafdar, An approach to fixedpoint theorems on uniform spaces, Trans Amer. Math Soc., 191, (1974), 209255.##[28] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Appl., 2012, (2012), 16.##]
The Integrating Factor Method in Banach Spaces
2
2
The so called integrating factor method, used to find solutions of ordinary differential equations of a certain type, is well known. In this article, we extend it to equations with values in a Banach space. Besides being of interest in itself, this extension will give us the opportunity to touch on a few topics that are not usually found in the relevant literature. Our presentation includes various illustrations of our results.
1

115
132


Josefina
Alvarez
Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003, USA.
Department of Mathematics, New Mexico State
Iran
jalvarez@nmsu.edu


Carolina
EspinozaVillalva
Departamento de Matem'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
Departamento de Matem'aticas, Universidad
Iran
carolina.espinoza@mat.uson.mx


Martha
GuzmanPartida
Departamento de Matem'aticas, Universidad de Sonora, Hermosillo, Sonora 83000, Mexico.
Departamento de Matem'aticas, Universidad
Iran
martha@mat.uson.mx
Banach spaces
CauchyRiemann integral
Exponential function
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Identification of Initial TaylorMaclaurin Coefficients for Generalized Subclasses of BiUnivalent Functions
2
2
In the present work, the author determines some coefficient bounds for functions in a new class of analytic and biunivalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].
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133
143


Arzu
Akgul
Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli, Turkey.
Department of Mathematics, Faculty of Arts
Iran
akgulcagla@hotmail.com
Analytic functions
Univalent functions
Biunivalent functions
TaylorMaclaurin series
Koebe function
Starlike and convex functions
Coefficient bounds
Polylogarithm functions
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