ORIGINAL_ARTICLE
Fixed Points of $p$-Hybrid $L$-Fuzzy Contractions
In this paper, the notion of $p$-hybrid $L$-fuzzy contractions in the framework of $b$-metric space is introduced. Sufficient conditions for existence of common $L$-fuzzy fixed points under such contractions are also investigated. The established ideas are generalizations of many concepts in fuzzy mathematics. In the case where our postulates are reduced to their classical variants, the concept presented herein merges and extends several significant and well-known fixed point theorems in the setting of both single-valued and multi-valued mappings in the corresponding literature of discrete and computational mathematics. A few of these special cases are pointed out and discussed. In support of our main hypotheses, a nontrivial example is provided.
https://scma.maragheh.ac.ir/article_244325_d30754f6d2c0cb3fb229dfc03729d6c5.pdf
2021-08-01
1
25
10.22130/scma.2021.137899.863
$b$-metric space
$L$-fuzzy set, $L$-fuzzy fixed point, $p$-hybrid $L$-fuzzy contraction, $L$-fuzzy set-valued map
Shehu Shagari
Mohammed
shagaris@ymail.com
1
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
LEAD_AUTHOR
Ibrahim
Fulatan
ialiy@abu.edu.ng
2
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
AUTHOR
Yahaya
Sirajo
surajmt95@gmail.com
3
School of Arts and Sciences, American University of Nigeria, Yola, Adamawa State, Nigeria.
AUTHOR
[1] M. Alansari, S.S. Mohammed, A. Azam and N. Hussain, On Multivalued Hybrid Contractions with Applications, J. Funct. Spaces, Vol. 2020, Article ID 8401403.
1
[2] A.E. Al-Mazrooei and J. Ahmad, Fixed point theorems for fuzzy mappings with applications, J. Intell. Fuzzy Syst., 36(4), (2019), pp. 3903-3909.
2
[3] A. Azam, M. Arshad and P. Vetro, On a pair of fuzzy $varphi$-contractive mappings, Math. Comput. Modelling, 52(2) (2010), pp. 207-214.
3
[4] A. Azam and I. Beg, Common fixed points of fuzzy maps, Math. Comput. Modelling, 49(7),(2009), pp. 1331-1336.
4
[5] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Functional Analysis, 30,(1989), pp. 26-37.
5
[6] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math., 3(1),(1922), pp. 133-181.
6
[7] V. Berinde, Generalized contractions in quasimetric spaces, In Seminar on Fixed Point Theory; Babes-Bolyai University: Cluj-Napoca, Romania, 1993, pp. 3–9.
7
[8] M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two $b$-metrics, Stud. Univ. Babeş-Bolyai, Math., 4(3), (2009), pp. 126-132.
8
[9] N. Bourbaki, Topologie Generale, Herman, Paris, France, 4(1),(1974), pp. 8-15.
9
[10] S. Czerwik, Contraction mappings in $ b $-metric spaces, Acta Math. Inform. Univ. Ostrav., 1(1), (1993), pp. 5-11.
10
[11] M.S. El Naschie, Wild topology, hyperbolic geometry and fusion algebra of high energy particle physics, Chaos Solitons Fractals, 13(9), (2002), pp. 1935-1945.
11
[12] M.S. El Naschie, On the unification of the fundamental forces and complex time in the $E^infty$ space, Chaos Solitons Fractals, 11(7), (2000), pp. 1149-1162.
12
[13] J.A. Goguen, $L$-fuzzy sets, J. Math. Anal. Appl., 18(1), (1967), pp. 145-174.
13
[14] S. Heilpern, Fuzzy mappings and fixed point theorem, J. Math. Anal. Appl., 83(2),(1981), pp. 566-569.
14
[15] N. Hussain, D. Doric, Z. Kadelburg and S. Radenovic, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012(1),(2012), pp. 126-134.
15
[16] N. Hussain and Z.D. Mitrović, On multi-valued weak quasi-contractions in $b$-metric spaces, Journal of Nonlinear Sciences and Applications, 10(7),(2017), pp. 3815-3823.
16
[17] T. Kamran, M. Samreen and Q. UL Ain, A generalization of $b$-metric space and some fixed point theorems, Mathematics, 5(2), (2017), pp. 19-26.
17
[18] H. Kaneko and S. Sessa, Fixed point theorems for compatible multi-valued and single-valued mappings, Int. J. Math. Comput. Sci., 12(2),(1989), pp. 257-262.
18
[19] E. Karapinar and A. Fulga, New Hybrid Contractions on $b$-Metric Spaces, Mathematics, 7(7), (2019), pp. 578-586.
19
[20] E. Karapinar, A short survey on the recent fixed point results on $b$-metric spaces, Constr. Math. Anal., 1(1), (2018), pp. 15-44.
20
[21] B.S. Lee, G.M. Sung, S.J. Cho and D.S. Kim, A common fixed point theorem for a pair of fuzzy mappings, Fuzzy Sets Syst., 98, (1998), pp.133-136.
21
[22] S.N. Mishra, S.L. Singh and R. Talwar, Nonlinear hybrid contractions on Menger and uniform spaces, Indian Journal of Pure and applied mathematics, 25,(1994), pp. 1039-1052.
22
[23] S.S. Mohammed and A. Azam, Fixed points of soft-set valued and fuzzy set-valued maps with applications, J. Intell. Fuzzy Syst., 37(3), (2019), pp. 3865-3877.
23
[24] S.B. Nadler, Multi-valued contraction mappings, Pac. J. Math., 30(2), (1969), pp. 475-488.
24
[25] S.A. Naimpally, S.L. Singh and J.H.M. Whitfield, Coincidence theorems for hybrid contractions, Math. Nachr., 127(1), (1986), pp.177-180.
25
[26] J.Y. Park and J.U. Jeong, (1997), pp. Fixed point theorems for fuzzy mappings, Fuzzy Sets Syst., 87(1), 111-116.
26
[27] H.K. Pathak, S.M. Kang and Y.J. Cho, Coincidence and fixed point theorems for nonlinear hybrid generalized contractions, Czech. Math. J., 48(2), (1998), pp. 341-357.
27
[28] V. Popa, Coincidence and fixed points theorems for noncontinuous hybrid contractions, In Nonlinear Analysis Forum, 7, (2002), pp. 153-158.
28
[29] D. Rakić, T. Došenović, Z.D. Mitrović, M. de la Sen and S. Radenović, Some fixed point theorems of Ćirić type in fuzzy metric spaces, Mathematics, 8(2), (2020), pp. 297-302.
29
[30] D. Rakić, A. Mukheimer, T. Došenović, Z.D. Mitrović and S. Radenović, On some new fixed point results in fuzzy $b$-metric spaces, J. Inequal. Appl., 2020(1), (2020),pp. 1-14.
30
[31] K.P. Rao, P.R. Swamy and J. R. Prasad, A common fixed point theorem in complex valued $b$-metric spaces, Bulletin of Mathematics and Statistics research, 1(1), (2013), pp. 1-8.
31
[32] M. Rashid, A. Azam and N. Mehmood, $L$-Fuzzy fixed points theorems for $L$-fuzzy mappings via $beta_{FL}$-admissible pair, The Scientific World Journal, Vol. 2014, Article ID 853032,(2014), 8 pages.
32
[33] M. Rashid, M.A. Kutbi and A. Azam, Coincidence theorems via alpha cuts of $L$-fuzzy sets with applications, Fixed Point Theory Appl., 2014(1), (2014), pp. 212-230.
33
[34] I.A. Rus, Generalized contractions and applications, Cluj University Press, 2(6),(2001), pp. 60-71.
34
[35] M.S. Shagari and A. Azam, Fixed point theorems of fuzzy set-valued maps with applications, Problemy Analiza, 9(27),(2020), pp. 2-17.
35
[36] C.T. Shieh and V.A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl., 347 (2008), pp. 266-272.
36
[37] S.L. Singh and B. Prasad, Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl., 55(11), (2008), pp. 2512-2520.
37
[38] L.A. Zadeh, Fuzzy sets, Inf. Control, 8(3), (1965), pp. 338-353.
38
ORIGINAL_ARTICLE
A Generalized Class of Univalent Harmonic Functions Associated with a Multiplier Transformation
We define a new subclass of univalent harmonic mappings using multiplier transformation and investigate various properties like necessary and sufficient conditions, extreme points, starlikeness, radius of convexity. We prove that the class is closed under harmonic convolutions and convex combinations. Finally, we show that this class is invariant under Bernandi-Libera-Livingston integral for harmonic functions.
https://scma.maragheh.ac.ir/article_244326_e055e5b960113742ca0491d26ac5329a.pdf
2021-08-01
27
39
10.22130/scma.2021.132155.841
Harmonic mapping
Convolution
Bernardi operator
Coefficient conditions
Extreme points
Deeplai
Khurana
deepali.02.08.88@gmail.com
1
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India.
AUTHOR
Raj
Garg
rajgarg2012@yahoo.co.in
2
Department of Mathematics, DAV University, Jalandhar-144001, Punjab, India.
LEAD_AUTHOR
Sarika
Verma
sarika.16984@gmail.com
3
Department of Mathematics, DAV University, Jalandhar-144001, Punjab, India.
AUTHOR
Gangadharan
Murugusundaramoorthy
gmsmoorthy@yahoo.com
4
School of Advanced Science,Vellore Institute of technology Deemed to be University, Vellore - 632014, India.
AUTHOR
[1] K. Al-Shaqsi, M. Darus and O. Abidemi, A New Subclass of Salagean-Type Harmonic Univalent Functions, Abstract and Appl. Ana., (2010), Article ID 821531, pp. 1-12.
1
[2] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math., 9 (1984), pp. 3-25.
2
[3] J.M. Jahangiri, Harmonic functions starlike in the unit disk, Journal of Mathematical Analysis and Applications, 235(2) (1999), pp. 470-477.
3
[4] J.M. Jahangiri, G. Murugusundaramoorthy, and K. Vijaya, Salagean type harmonic functions, Southwest J. Pure Appl. Math., 2(2002), pp. 77-82.
4
[5] R. Kumar, S. Gupta and S. Singh, A class of univalent harmonic functions defined by multiplier transformation, Rev. Roumaine Math. Pures Appl., 57 (2012), pp. 371-382.
5
[6] H. Lewy, On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Soc., 42 (1936), pp. 689-692.
6
[7] T.O. Opoola, On a new subclass of univalent functions, Mathematica, 36(59) (1994), pp. 195-200.
7
[8] G.S. Salagean, Subclasses of univalent functions, Lecture Notes in Math., Springer - Verlag, Heidlberg, 1013 (1983), pp. 362-372.
8
[9] H. Silverman, Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl., 220 (1998), pp. 283-289.
9
[10] E. Yasar and S. Yalcin, Harmonic univalent functions starlike or convex of complex order, Tamsui Oxford Journal of Information and Mathematical Sciences, 27(3) (2011), pp. 269-277.
10
ORIGINAL_ARTICLE
On Some Linear Operators Preserving Disjoint Support Property
The aim of this work is to characterize all bounded linear operators $T:\lpi\rightarrow\lpi$ which preserve disjoint support property. We show that the constant coefficients of all isometries on $\lpi$ are in the class of such operators, where $2\neq p\in [1,\infty )$ and $I$ is a non-empty set. We extend preserving disjoint support property to linear operators on $\mathfrak{c}_{0}(I).$ At the end, we obtain some equivalent properties of isometries on Banach spaces.
https://scma.maragheh.ac.ir/article_244939_8c1b7702456136d5bdd669a1216f6552.pdf
2021-08-01
41
49
10.22130/scma.2021.115697.690
Disjoint support
Codomain
Linear preserver
Isometry
Noha
Eftekhari
eftekharinoha@yahoo.com
1
Department of pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P.O.Box 115, Shahrekord, 88186-34141, Iran.
LEAD_AUTHOR
Ali
Bayati Eshkaftaki
bayati.ali@sku.ac.ir
2
Department of pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P.O.Box 115, Shahrekord, 88186-34141, Iran.
AUTHOR
[1] Y.A. Abramovich and A.K. Kitover, Inverses of disjointness preserving operators, Mem. Amer. Math. Soc., 143 (2000), pp. 1-162.
1
[2] Y.A. Abramovich, A.I. Veksler and A.V. Koldunov, Operators preserving disjointness, Dokl. Akad. Nauk USSR, 248 (1979), pp. 1033-1036.
2
[3] T. Ando, Majorization and inequalities in matrix theory, Linear Algebra Appl., 199 (1994), pp. 17-67.
3
[4] F. Bahrami, A. Bayati and S.M. Manjegani, Linear preservers of majorization on $lpi$, Linear Algebra Appl., 436 (2012), pp. 3177-3195.
4
[5] S. Banach, Theorie des operations lineares, Chelsea, Warsaw, 1932.
5
[6] N.L. Carothers, A Short course on Banach space theory, Cambridge University Press, 2005.
6
[7] J.T. Chan, Operators with the disjoint support property, J. Operator Theory, 24 (1990), pp. 383-391.
7
[8] R.J. Fleming and J.E. Jamison, Isometries on Banach spaces: vector-valued function spaces, Vol. 2, Taylor and Francis Group, LLC, 2008.
8
[9] H-L. Gau, J-S. Jeang and N-C. Wong, Biseparating linear maps between continuous vector-valued function spaces, J. Aust. Math. Soc., 74 (2003), pp. 101-109.
9
[10] J-S. Jeang and N-C. Wong, Weighted composition operators of $C_0(X)$'s, J. Math. Anal. Appl., 201 (1996), pp. 981-993.
10
[11] A. Jimenez-Vergas and Ya-Shu Wang, Linear biseparating maps between vector-valued little Lipschitz function spaces, Acta Math. Sin. (Engl. Ser. ), 26 (2010), pp. 1005-1018.
11
[12] J. Lamperti, On the isometries of certain function-spaces, Pacific J. Math., 8 (1958), pp. 459-466.
12
[13] S. Pierce, A survey of linear preserver problems, Linear Multilinear Algebra, 33 (1992), pp. 1-2.
13
[14] B.Z. Volkh, On linear multiplicative operations, Dokl. Akad. Nauk USSR, 41 (1943), pp. 148-151.
14
[15] H. Zhang, Orthogonality from disjoint support in reproducing kernel Hilbert spaces, J. Math. Anal. Appl., 349 (2009), pp. 201-210.
15
ORIGINAL_ARTICLE
Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces
The present paper seeks to prove the existence and uniqueness of solutions to stochastic evolution equations in Hilbert spaces driven by both Poisson random measure and Wiener process with non-Lipschitz drift term. The proof is provided by the theory of measure of noncompactness and condensing operators. Moreover, we give some examples to illustrate the application of our main theorem.
https://scma.maragheh.ac.ir/article_244940_dba1e68bdd5e1765959ed2e089f27abc.pdf
2021-08-01
51
68
10.22130/scma.2021.520720.884
Poisson random measure
Mild solution
Measure of noncompactness
Condensing operator
Majid
Zamani
mjdzamani@aut.ac.ir
1
Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran.
AUTHOR
S. Mansour
Vaezpour
vaez@aut.ac.ir
2
Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran.
LEAD_AUTHOR
Erfan
Salavati
erfan.salavati@aut.ac.ir
3
Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran.
AUTHOR
[1] R.R. Akhmerov, M.I. Kamenskii, A.S. Patapov, A.E. Rodkina and B.N. Sadovskii, Measures of noncompactness and condensing operators, Birkhäuser--Verlag, Basel, Switzerland, 1992.
1
[2] S. Albeverio, V. Mandrekar and B. Rudiger, Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Levy noise, Stochastic Process. Appl., 119 (2009), pp. 835-863.
2
[3] A. Anguraj and K. Banupriya, Existence, uniqueness and stability results for impulsive stochastic functional differential equations with infinite delay and Poisson jumps, Malaya J., 5 (2017), pp. 653-659.
3
[4] D. Barbu, Local and global existence for mild solutions of stochastic differential equations, Port. Math., 55 (1998), pp. 411-424.
4
[5] D. Barbu and G. Bocsan, Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients, Czechoslovak Math. J., 52 (2002), pp. 87-95.
5
[6] D. Barbu and G. Bocsan, Successive approximations to solutions of stochastic semilinear functional differential equations in Hilbert spaces, Technical Report 162, University of Timisoara, Faculty of Mathematics, STPA - Seminar of Probability Theory and Applications, Timișoara, Romania, 2004.
6
[7] Z. Brzezniak, E. Hausenblas and P.A. Razafimandimby, Stochastic reaction-diffusion equations driven by jump processes, Potential Anal., 49 (2018), pp. 131-201.
7
[8] G. Cao and K. He, Successive approximation of infinite dimensional semilinear backward stochastic evolution equations with jumps, Stochastic Process. Appl., 117 (2007), pp. 1251-1264.
8
[9] G. Da Prato and F. Flandoli, Pathwise uniqueness for a class of SDE in Hilbert spaces and applications, J. Funct. Anal., 259 (2010), pp. 243-267.
9
[10] G. Da Prato, F. Flandoli, M. Rockner and A.Y. Veretennikov, Strong uniqueness for SDEs in Hilbert spaces with nonregular drift, Ann. Probab., 44 (2016), pp. 1985-2023.
10
[11] G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions, Cambridge University Press, Cambridge, UK, 2014.
11
[12] X.L. Fan, Non autonomous semilinear stochastic evolution equations, Comm. Statist. Theory Methods, 44 (2015), pp. 1806-1818.
12
[13] L. Guedda and P.R. Fitte, Existence and dependence results for semilinear functional stochastic differential equations with infinite delay in a Hilbert space, Mediterr. J. Math., 13 (2016), pp. 4153-4174.
13
[14] E. Hausenblas, Existence, uniqueness and regularity of parabolic SPDEs driven by Poisson random measure, Electron. J. Probab., 10 (2005), pp. 1496-1546.
14
[15] E. Hausenblas, SPDEs driven by Poisson random measure with non-Lipschitz coefficients: existence results, Probab. Theory Related Fields, 137 (2007), pp. 161-200.
15
[16] E. Hausenblas and J. Seidler, Stochastic convolutions driven by martingales: maximal inequalities and exponential integrability, Stoch. Anal. Appl., 26 (2007), pp. 98-119.
16
[17] A. Jakubowski, M. Kamenskii and P.R. Fitte, Existence of weak solutions to stochastic evolution inclusions, Stoch. Anal. Appl., 23 (2005), pp. 723-749.
17
[18] E. Pardoux, Stochastic partial differential equations and filtering of diffusion propcesses, Stochastics, 6 (1979), pp. 193-231.
18
[19] S. Peszat and J. Zabczyk, Stochastic partial differential equations with Levy noise: An evolution equation approach, Cambridge University Press, Cambridge, UK, 2007.
19
[20] M. Rockner and T. Zhang, Stochastic evolution equations of jump type: existence, uniqueness and large deviation principles, Potential Anal., 26 (2007), pp. 255-279.
20
[21] T. Taniguchi, Successive approximations to solutions of stochastic differential equations, J. Differ. Equ., 96 (1992), pp. 152-169.
21
[22] T. Taniguchi, Successive approximations to solutions of stochastic differential equations, J. Differ. Equ., 96 (1992), pp. 152-169.
22
[23] L. Wang, The existence and uniqueness of mild solutions to stochastic differential equations with Levy noise, Adv. Differ. Equ., 2017 (2017), pp. 1-12.
23
[24] B. Xie, Stochastic differential equations with non-Lipschitz coefficients in Hilbert spaces, Stoch. Anal. Appl., 26 (2008), pp. 408-433.
24
[25] T. Yamada, On the successive approximation of solutions of stochastic differential equations, J. Math. Kyoto Univ., 21 (1981), pp. 501-515.
25
ORIGINAL_ARTICLE
Bicomplex Frames
We define in a natural way the bicomplex analog of the frames (bc-frames) in the setting of bicomplex infinite Hilbert spaces, and we characterize them in terms of their idempotent components. We also extend some classical results from frames theory to bc-frames and show that some of them do not remain valid for bc-frames in general. The construction of bc-frame operators and Weyl--Heisenberg bc-frames are also discussed.
https://scma.maragheh.ac.ir/article_244941_28312fad14c7968bb218915ac76a0ec2.pdf
2021-08-01
69
89
10.22130/scma.2021.140216.875
Bicomplex
bc-frames
bc-frame operator
Weyl-Heisenberg bc-frame
Aiad
Elgourari
aiadelgourari@gmail.com
1
Lab. P.D.E., Algebra and Spectral Geometry, Department of mathematics, Faculty of sciences, P.O.Box 133, Ibn Tofail University in Kenitra; Morocco.
LEAD_AUTHOR
Allal
Ghanmi
allalghanmi@um5.ac.ma
2
Analysis, P.D.G $\&$ Spectral Geometry. Lab. M.I.A.-S.I., CeReMAR, Department of Mathematics, P.O. Box 1014, Faculty of Sciences, Mohammed V University in Rabat, Morocco.
AUTHOR
Mohammed
Souid El Ainin
msouidelainin@yahoo.fr
3
Faculty of Law, Economics and Social Sciences, Ibn Zohr University, Agadir, Morocco.
AUTHOR
[1] D.S. Alexiadis and G.D. Sergiadis, Estimation of motions in color image sequences using hypercomplex Fourier transforms, IEEE Trans. Image Process., 18 (1) (2009), pp. 168-187.
1
[2] P. Balazs, N. Holighaus, T. Necciari and D. Stoeva, Frame theory for signal processing in psychoacoustics, in: Excursions in harmonic analysis, vol.5, Appl. Numer. Harmon. Anal., Birkhauser, Springer, Cham, 2017, pp. 225-268.
2
[3] J.J. Benedetto, Irregular sampling and frames in Wavelets, in: A Tutorial in Theory and Applications, Chui. C.K. ed. Cambridge, MA. Academic Press, 1992, pp. 445-507.
3
[4] H. Bolcskei, F. Hlawatsch and H.G. Feichtinger, Frame-theoretic analysis of oversampled filter banks, IEEE Trans. Signal Process., 46 (12) (1998), pp. 3256-3268.
4
[5] P.G. Casazza, The art of frame theory, Taiwanese J. Math., 4 (2) (2000), pp. 129-202.
5
[6] P.G. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math., 345 (2004), pp. 87-113.
6
[7] P.G. Casazza and R.G. Lynch, A brief introduction to Hilbert space frame theory and its applications, Finite frame theory, Proc. Sympos. Appl. Math., 73 (2016), pp. 1-51.
7
[8] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, 2016.
8
[9] I. Daubechies, Ten Lectures on Wavelets, Philadelphia. SIAM, 1992.
9
[10] I. Daubechies, The wavelet transformation, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory., 36 (1990), pp. 961-1005.
10
[11] I. Daubechies, A. Grassmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Physics., 27 (1986), pp. 1271-1283.
11
[12] B. Deng, W. Schempp, C. Xiao and Z. Wu, On the existence of Weyl-Heisenberg and affine frames, Preprint, 1997.
12
[13] D.L. Donoho and M. Elad, Optimally sparse representation in general (nonorthogonal) dictionaries via $l^1$ minimization, in: Proc. Natl. Acad. Sci. USA, 100 (5) (2003), pp. 2197-2202.
13
[14] R. Duffin and A. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366.
14
[15] Y.C. Eldar and G.D. Jr Forney, Optimal tight frames and quantum measurement, IEEE Trans. Inf. Theory., 48 (3) (2002), pp. 599-610.
15
[16] A. El Gourari, A. Ghanmi and K. Zine, On bicomplex Fourier-Wigner transforms, Int. J. Wavelets Multiresolut. Inf. Process., 18 (3) (2020), 2050008, 16 pages.
16
[17] M.T. El-Melegy and A.T. Kamal, Color Image Processing Using Reduced Biquaternions With Application to Face Recognition in a PCA Framework, Proc. IEEE Inte. Conf. Computer Vision (ICCV)., (2017), pp. 3039-3046.
17
[18] T.A. Ell and S.J. Sangwine, Hypercomplex Fourier transforms of color images, IEEE Trans. Image Process., 16 (1) (2007), pp. 22-35.
18
[19] M. Frank and D.R. Larson, Frames in Hilbert $C^*$--modules and $C^*$-algebras, preprint, University of Houston and Texas A$&$M University, Texas, U.S.A., 1998.
19
[20] M. Frank and D.R. Larson, A module frame concept for Hilbert $C^*$-modules, in: the Functional and Harmonic Analysis of Wavelets and frames, Contemp. Math., 247, (1999), pp. 207-233.
20
[21] M. Frank and D.R. Larson, Modular frames for Hilbert $C^*$-modules and symmetric approximation of frames, Proc. SPIE., 4119 (2000), pp. 325-336.
21
[22] M. Frank and D.R. Larson, Frames in Hilbert $C^*$-modules and $C^* $-algebras, J. Operator Theory., 2 (48) (2002), pp. 273-314.
22
[23] P. Gavruta, On some identities and inequalities for frames in Hilbert spaces, J. Math. Anal. Appl., 321 (2006), pp. 469-478.
23
[24] R. Gervais Lavoie, L. Marchildon and D. Rochon, Infinite dimensional bicomplex Hilbert spaces, Ann. Funct. Anal., 2 (2010), pp. 75-91.
24
[25] A. Ghanmi and K. Zine, Bicomplex analogs of Segal-Bargmann and fractional Fourier transforms, Adv. Appl. Clifford Algebr., 29 (4) (2019), 20 pages.
25
[26] K. Grochenig, Foundations of Time-Frequency Analysis, Birkhauser, Boston 2001.
26
[27] E. Guariglia and S. Silvestrov, Fractional-wavelet analysis of positive definite distributions and wavelets on $D'(mathbb{C})$, in: Engineering Mathematics II, Springer Proc. Math. Stat., 179, Springer, Cham, 2016, pp. 337-353.
27
[28] C. Heil and D. Walnut, Continuous and discrete wavelet transforms, SIAM Rev., 31 (1989), pp. 628-666 .
28
[29] C. Heil, A Basis Theory Primer, Birkhauser, Boston, 2010.
29
[30] M. Joita, Tensor products of Hilbert modules over locally $C^*$-algebras, Czechoslovak Math. J., 54 (129) (2004), pp. 727-737.
30
[31] A. Khosravi and B. Khosravi, Frames and bases in tensor products of Hilbert spaces and Hilbert $C^*$-modules, Proc. Indian Acad. Sci. Math. Sci., 117 (1) (2007), pp. 1-12.
31
[32] A. Khosravi and B. Khosravi, Fusion frames and $g$-frames in Hilbert $C^*$-modules, Int. J. Wavelet. Multiresolut. Inf. Process., 6 (3) (2008), pp. 433-446.
32
[33] J. Kovacevic and A. Chebira, An introduction to frames, Found. Trends Signal Process., 2 (1) (2008), pp. 1-94.
33
[34] C.E. Moxey, S.J. Sangwine and T. Ell, A. Hypercomplex correlation techniques for vector images, IEEE Trans. Signal Process., 51 (7) (2003), pp. 1941-1953.
34
[35] G.B. Price, An Introduction to Multicomplex Spaces and Functions, Monographs and Textbooks, Pure and Appl Math., 140, Marcel Dekker Inc., New York, 1991.
35
[36] I. Raeburn and S.J. Thompson, Countably generated Hilbert modules, the Kasparov stabilisation theorem, and frames with Hilbert modules, Proc. Amer. Math. Soc., 131 (5) (2003), pp. 1557-1564.
36
[37] D. Rochon and M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers, An Univ. Oradea Fasc. Mat., 11 (2004), pp. 71-110.
37
[38] D. Rochon and S. Tremmblay, Bicomplex quantum mechanics, I: The generalized Schrodinger equation, Adv. Appl. Clifford Algebr., 14 (2004), pp. 231-248.
38
[39] D. Rochon and S. Tremmblay, Bicomplex quantum mechanics, II: The Hilbert space, Adv. Appl. Clifford Algebr., 16 (2006), pp. 135-157.
39
[40] J. Wu, Frames in Hilbert $C^*$-modules, Electronic Theses and Dissertations, 899, pp. 2004-2019.
40
[41] R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press, New York, 1980.
41
[42] M. Zaied, O. Jemai and C. Ben Amar, Training of the Beta wavelet networks by the frames theory: Application to face recognition, in: first Workshops on Image Processing Theory, Tools and Applications, 2008, pp. 1-6.
42
ORIGINAL_ARTICLE
Integral $K$-Operator Frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$
In this work, we introduce a new concept of integral $K$-operator frame for the set of all adjointable operators from a Hilbert $C^{\ast}$-module $\mathcal{H}$ to itself denoted by $End_{\mathcal{A}}^{\ast}(\mathcal{H}) $. We give some properties relating to some constructions of integral $K$-operator frames and to operators preserving integral $K$-operator frame and we establish some new results.
https://scma.maragheh.ac.ir/article_245093_07dd1360b8edf8b60112e040dfd1a67b.pdf
2021-08-01
91
107
10.22130/scma.2021.140176.874
K-frames
integral K-operator frames
$C^{ast}$-algebra
Hilbert $mathcal{A}$-module
Hatim
Labrigui
hlabrigui75@gmail.com
1
Department of Mathematics, Faculty of Science, University of Ibn Tofail, B.P. 133, Kenitra, Morocco.
LEAD_AUTHOR
Samir
Kabbaj
samkabbaj@yahoo.fr
2
Department of Mathematics, Faculty of Science, University of Ibn Tofail, B.P. 133, Kenitra, Morocco.
AUTHOR
[1] S.T. Ali, J.-P Antoine and J.-P. Gazeau, Continuous frames in Hilbert space, Ann. Phy., {222} (1993), pp. 1-37.
1
[2] A. Alijani and M.A. Dehghan, $ast$-Frames in Hilbert $mathcal{C}^{ast}$-modules, U.P.B. Sci. Bull., Series A, {73} (2011), pp. 89-106.
2
[3] L. Arambasic, On frames for countably generated Hilbert $mathcal{C}^{ast}$-modules, Proc. Amer. Math. Soc., {135} (2007), pp. 469-478.
3
[4] O. Christensen, An Introduction to Frames and Riesz Bases, Brikh$ddot{a}$user, Boston, 2003.
4
[5] J.B. Conway, A Course In Operator Theory, Amer. Math. Soc., Rhode Island, 2000.
5
[6] K.R. Davidson, $mathcal{C}^{ast}$-algebra by example, Amer. Math. Soc., Rhode Island, 1996.
6
[7] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366.
7
[8] M. Frank and D.R. Larson, Frames in Hilbert $mathcal{C}^{ast}$-modules and $mathcal{C}^{ast}$-algebras, J. Operator Theory, 48 (2002), pp. 273-314.
8
[9] J.P. Gabardo and D. Han, Frames associated with measurable spaces, Adv. Compu. Math., 18 (2003), pp. 127-147.
9
[10] L. G$breve{a}$vruta, Frames for operators, Appl. Comput. Harmon. Anal., 32 (2012), pp. 139-144.
10
[11] I. Kaplansky, Modules over operator algebras, Amer. J. Math., 75 (1953), pp. 839-858.
11
[12] A. Khosravi and B. Khosravi, Frames and bases in tensor products of Hilbert spaces and Hilbert $mathcal{C}^{ast}$-modules, Proc. Indian Acad. Sci. Math. Sci., 117 (2007), pp. 1-12.
12
[13] A. Najati, M. Mohammadi Saem and P. G$breve{a}$vruta, Frames and operators in Hilbert $mathcal{C}^{ast}$-modules, Oper. Matrices, 10 (2016), pp. 73-81.
13
[14] W.L. Paschke, Inner product modules over $B^{ast}$-algebras, Trans. Amer. Math. Soc., 182 (1973), pp. 443-468.
14
[15] M. Rossafi and A. Akhlidj, Perturbation and stability of operator Frame for $End_{mathcal{A}}^{ast}(mathcal{H})$,
15
Math-Recherche and Applications, 16(1) (2018), pp. 65-81.
16
[16] M. Rossafi, F. Chouchene and S. Kabbaj, Integral Frame in Hilbert $C^{ast}$-module, arXiv:2005.09995v2 [math.FA] 30 Nov 2020.
17
[17] M. Rossafi and S. Kabbaj, $K$-operator Frame for $End_{mathcal{A}}^{ast}(mathcal{H})$, Asia Mathematika, 2(2) (2018), pp. 52-60.
18
[18] M. Rossafi and S. Kabbaj, Operator Frame for $End_{mathcal{A}}^{ast}(mathcal{H})$, J. Linear. Topological. Algebra., 8(2) (2019), pp. 85-95.
19
[19] K. Yosida, Functional Analysis, Springer-Verlag, Germany, 1980.
20
[20] L.C. Zhang, The factor decomposition theorem of bounded generalized inverse modules and their topological continuity, J. Acta Math. Sin., 23 (2007), pp. 1413-1418.
21
ORIGINAL_ARTICLE
Characteristics of Solutions of Fractional Hybrid Integro-Differential Equations in Banach Algebra
In this paper, we discuss the existence results for a class of hybrid initial value problems of Riemann-Liouville fractional differential equations. Our investigation is based on the Dhage hybrid fixed point theorem, remarks and some special cases will be discussed. The continuous dependence of the unique solution on one of its functions will be proved.
https://scma.maragheh.ac.ir/article_245096_db0e04a3c16285e17ecf58580ada2ec3.pdf
2021-08-01
109
131
10.22130/scma.2021.120867.876
Hybrid differential equations
Quadratic differential equation
Dhage hybrid fixed point theorem
Banach algebra
Ahmed
El-Sayed
amasayed@alexu.edu.eg
1
Department of mathematics, Alexandria University, Alexandria, Egypt.
AUTHOR
Hind
Hashem
3922@qu.edu.sa
2
Department of mathematics, College of Science, Qassim University, P.O. Box 6644 Buraidah 51452 , Saudi Arabia.
AUTHOR
Shorouk
Al-Issa
shorouk.alissa@liu.edu.lb
3
Department of mathematics, Lebanese International University, Lebanon, Saida.
LEAD_AUTHOR
[1] B. Ahmad, S.K. Ntouyas and J. Tariboon, A nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations, Acta Math. Sci., 36(6) (2016),pp. 1631-1640.
1
[2] S. Abbas, Existence of solutions to fractional order ordinary and delay differential equations and applications, Electron. J. Differ. Equ., 2011(9) (2011), pp. 1-11.
2
[3] Sh.M Al-Issa and N.M. Mawed, Results on solvability of nonlinear quadratic integral equations of fractional orders in Banach algebra, J. Nonlinear Sci. Appl.,14(4) (2021), pp. 181-195.
3
[4] J. Banas and B. Rzepka, Monotonic solutions of a quadratic integral equation of fractional order, J. Math. Anal. Appl., 332(2) (2007), pp. 1371-1379.
4
[5] B.C. Dhage, A fixed point theorem in Banach algebras involving three operators with applications, Kyungpook Math. J., 44(1) (2004), pp. 145–155.
5
[6]B.C. Dhage andB.D. Karande, First order integro-differential equations in Banach algebras involving Caratheodory and discontinuous nonlinearities, Electron. J. Qual. Theory Differ. Equ., 2005(21) (2005), pp. 1-16.
6
[7] B.C. Dhage and V. Lakshmikantham, Basic results on hybrid differential equation, Nonlinear Anal. Hybrid Syst.,4(3) (2010), pp. 414-424.
7
[8] M.A. Darwish and K. Sadarangani, Existence of solutions for hybrid fractional pantograph equations, Appl. Anal. Discrete Math.,9 (2015), pp. 150-167.
8
[9] A.M.A. El-Sayed, F.M. Gaafar and H.H.G. Hashem, On the maximal and minimal solutions of arbitrary-orders nonlinear functional integral and differenbtial equations, Math. Sci. Res. J.,8(11), (2004), pp. 336-348.
9
[10] A.M.A El-Sayed and H.H.G. Hashem, Integrable and continuous solutions of a nonlinear quadratic integral equation, Electron. J. Qual. Theory Differ. Equ., 2008(25) (2008), pp. 1-10.
10
[11] A.M.A El-Sayed and H.H.G. Hashem, Monotonic solutions of functional integral and differential equations of fractional order, Electron. J. Qual. Theory Differ. Equ., 2009(2009), pp. 1-8.
11
[12] A.M.A El-Sayed and H.H.G. Hashem, Existence results for nonlinear quadratic integral equations of fractional order in Banach algebra, Fract. Calc. Appl. Anal., 16(4) (2013), pp. 816-826.
12
[13] A.M.A. El-Sayed, Sh.M Al-Issa and N.M. Mawed, On A Coupled System of Hybrid Fractional-order Differential Equations in Banach Algebras, Adv. Dyn. Syst. Appl., 16(1) (2021),pp. 91-112.
13
[14]A.R Elsonbatyand A.M.A El-Sayed, Further nonlinear dynamical analysis of simple jerk system with multiple attractors,
14
Nonlinear Dynamics,87(2) (2017), pp. 1169-1186.
15
[15] F.M. Gaafar, Positive solutions of a quadratic integro-differential equation, J. Egyptian Math. Soc., 22(2) ( 2014), pp. 162-166.
16
[16] M.A.E. Herzallah and D. Baleanu,On Fractional Order Hybrid Differential Equations, Abstr. Appl. Anal., 2014 (2014), 7 pages.
17
[17] H. Lu, S. Sun, D. Yang and H. Teng, Theory of fractional hybrid differential equations with linear perturbations of second type, Bound. Value Probl.,2013(23)(2013), 16 pages.
18
[18] E. H. Rothe, Topological Methods in the Theory of Nonlinear Integral Equations, Amer. Math. Monthly, 75(3) ( 1968), pp. 318-319.
19
[19] S. Sitho, S. K. Ntouyas and J. Tariboon, Existence results for hybrid fractional integro-differential equations, Bound. Value Probl., 2015(113) (2015), 13 pages.
20
[20] L. Zheng andX. Zhang, Modeling and analysis of modern fluid problems, Math. Sci. Eng, Academic Press, London, 2017.
21
[21] Y. Zhao, S. Suna, Z. Hana andQ. Li, Theory of fractional hybrid differential equations, Comput. Math. Appl., 62(3) (2011), pp. 1312-1324.
22
ORIGINAL_ARTICLE
Woven g-Fusion Frames in Hilbert Spaces
In this paper, we introduce the notion of woven g-fusion frames in Hilbert spaces. Then, we present sufficient conditions for woven g-fusion frames in terms of woven frames in Hilbert spaces. We extend some of the recent results of standard woven frames and woven fusion frames to woven g-fusion frames. Also, we study perturbations of woven g-fusion frames.
https://scma.maragheh.ac.ir/article_245656_84649d2e0770efe44077b193828a8a3a.pdf
2021-08-01
133
151
10.22130/scma.2021.137940.870
Frame
G-fusion Frame
Woven frame
Weaving g-fusion frame
Perturbation
Maryam
Mohammadrezaee
dr.rezaee.bst@gmail.com
1
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
AUTHOR
Mehdi
Rashidi-Kouchi
rashidimehdi20@gmail.com
2
Department of Mathematics, Ghaderabad Center, Islamic Azad University, Ghaderabad, Iran.
LEAD_AUTHOR
Akbar
Nazari
nazari@mail.uk.ac.ir
3
Department of Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
AUTHOR
Ali
Oloomi
ali_oloomi111@yahoo.com
4
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
AUTHOR
[1] M.S. Asgari and A. Khosravi, Frames and bases of subspaces in Hilbert spaces, J. Math. Anal. Appl., 308 (2005),pp. 541-553.
1
[2] T. Bemrose, P.G. Casazza, K. Grochenig, M.C. Lammers and R.G. Lynch, Weaving Frames, J. Oper. Matrices., 10 (2016), pp. 1093-1116.
2
[3] P.G. Casazza, D. Freeman and R.G. Lynch, Weaving Schauder frames, J. Approx. Theory., 211 (2016), pp. 42-60.
3
[4] P.G. Casazza and G. Kutyniok, Frames of Subspaces, Contemp Math. Amer. Math. Soc., 345, (2004), pp. 87-113.
4
[5] P.G. Casazza, G. Kutyniok and Sh. Li, Fusion frames and distributed processing, Appl. Comput. Harmon. Anal., 25 (2008), pp. 114-132.
5
[6] P.G. Casazza and R.G. Lynch, Weaving properties of Hilbert space frames, J. Proc. SampTA., (2015), pp. 110-114.
6
[7] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, Boston, (2016).
7
[8] I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 1271-1283.
8
[9] Deepshikha and L.K. Vashisht, Weaving K-frames in Hilbert spaces, Results Math., 73 (2018), pp. 1-20.
9
[10] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72, (1952), pp. 341-366.
10
[11] D. Han and D. Larson, Frames, bases and group representations, Mem. Amer. Math. Soc., 147 (697) (2000).
11
[12] A. Khosravi and M.S. Asgari, Frames of subspaces and approximation of the inverse frame operator, Houston. J. Math., 33 (2007), pp. 907-920.
12
[13] A. Khosravi and K. Musazadeh, Fusion frames and g-frames, J. Math. Anal. Appl., 342 (2008), pp. 1068-1083.
13
[14] A. Khosravi and J. Sohrabi Banyarani, Weaving $g$-frames and weaving fusion frames, Bull. Malays. Math. Sci. Soc., 42 (2019), pp. 3111-3129.
14
[15] R. Rezapour, A. Rahimi, E. Osgooei and H. Dehghan, Controlled weaving frames in Hilbert spaces, Inf. Dim. Anal. Quan. Prob. Rel. Top., 22 (2019), pp. 1-18.
15
[16] V. Sadri, Gh. Rahimlou, R. Ahmadi and R. Zarghami Farfar, Generalized Fusion Frames in Hilbert Spaces, Inf. Dim. Anal. Quan. Prob. Rel. Top., (to appear).
16
[17] W. Sun, g-frames and g-Riesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437-452.
17
[18] L.K. Vashisht and Deepshikha, On continuous weaving frames, Adv. Pure Appl. Math., 8 (2017), pp. 15-31.
18
[19] L.K. Vashisht and Deepshikha, Weaving properties of generalized continuous frames generated by an iterated function system, J. Geom. Phys., 110 (2016), pp. 282-295.
19
[20] L.K. Vashisht and Deepshikha, S. Garg and G. Verma , On weaving fusion frames for Hilbert spaces, In: Proceedings of SampTA., (2017), pp. 381-385.
20
ORIGINAL_ARTICLE
A Review on Some Fuzzy Integral Inequalities
In this paper, we introduce fuzzy measure and fuzzy integral concepts and express some of the fuzzy integral properties. The main purpose of this article is to reviewing of some important mathematical inequalities that have many applications in modeling mathematical problems. Firstly, we prove the related Gauss-Winkler type inequality for fuzzy integrals. Indeed, we prove fuzzy version provided by D. H. Hong. Another the famous mathematical inequality is Minkowski's inequality. It is an important inequality from both mathematical and application points of view. Here, we state a Minkowski type inequality for fuzzy integrals. The established results are based on the classical Minkowski's inequality for integrals. In the continue, we showed that by an example the classical Pr\'{e}kopa-Leindler type inequality is not valid for the Sugeno integral. We proved one version of the Pr\'{e}kopa-Leindler type inequality by adding concave fuzzy measure and quasi-concave fuzzy measure assumptions for the Sugeno integral with different proofs. Also, we obtained a derivation version of the Pr\'{e}kopa-Leindler inequality and illustrated all of the main results by examples. Finally, we investigate the Thunsdorff's inequality for Sugeno integral. By an example, we show that the classical form of this inequality does not hold for the Sugeno integral. Then, by reviewing the initial conditions, we prove two main theorems for this inequality.By checking the special case of the aforementioned Thunsdorff's inequality, we prove Frank-Pick type inequality for the Sugeno integral and illustrate it by an example.
https://scma.maragheh.ac.ir/article_252670_81847809bb775ee02a7be32cea2fbfd9.pdf
2021-08-01
153
185
10.22130/scma.2022.555219.1125
Set-valued functios
Sugeno integral
Gauss-Winkler inequality
Minkowski's inequality
Pr'{e}kopa-Leindler's inequality
Thunsdorff's inequality
Frank-Pick's inequality
Fuzzy integral inequality
Bayaz
Daraby
bdaraby@maragheh.ac.ir
1
Department of Mathematics, University of Maragheh, P. O. Box 55181-83111, Maragheh, Iran.
LEAD_AUTHOR
[1] H. Agahi and M. A. Yaghoobi, A Minkowski type inequality for fuzzy integrals, Journal of Uncertain Systems, 4 (3) (2010), pp. 187-194.
1
[2] H. Agahi, Y. Ouyang, R. Mesiar, E. Pap and M. Strboja, Holder and Minkowski type inequalities for pseudo-integral, Appl. Math. Comput., 217 (2011), pp. 8630-8639.
2
[3] R.P. Agarwal and S.S. Dragomir, An application of Hayashiâs inequality for differentiable functions, Comput. Math. Appl., 32 (1996), pp. 95-99.
3
[4] N. Balakrishnan and T. Rychlik, Evaluating expectation sof L-statistics by the Steffensen inequality, Metrika, 63(3) (2006), pp. 371-384.
4
[5] L. Bougoffa, On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, 7(2) (2006), article 60.
5
[6] P.S. Bullen, A dictionary of inequalities, Addison Wesley Longman Inc, (1998).
6
[7] J. Caballero and K. Sadarangani, Fritz Carlsonas inequality for fuzzy integrals, Comput. Math. Appl., 59(8) (2010), pp. 2763-2767.
7
[8] T.Y. Chen, H.L. Chang and G.H. Tzeng, Using fuzzy measures and habitual domains to analyze the public attitude and apply to the gas taxi policy, Eur. J. Oper. Res., 137 (2002), pp. 145-161.
8
[9] D. Cordero-Erausquin, R.J. Mc-Cann and M. Schmuckenschlaager, Prekopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields and optimal transport, Annals de la Faculte des sciences de Toulouse, XV (4) (2006), pp. 613-635.
9
[10] B. Daraby, Investigation of a Stolarsky type inequality for integrals in pseudo-analysisFractional, Fract. Calc. Appl. Anal., 13 (5) (2010), pp. 467-473.
10
[11] B. Daraby, Generalization of the Stolarsky type inequality for pseudo-integrals, Fuzzy Sets Syst., 194 (1) (2012), pp. 90-96.
11
[12] B. Daraby, Generalization of the Stolarsky type inequality for pseudo-integrals, Fuzzy Sets Syst., 194 (2012), pp. 90-96.
12
[13] B. Daraby, Markov type integral inequality for Pseudo-integrals, Casp. J. Appl. Math. Ecol. Econ., 1 (1) 2013, pp. 13-23.
13
[14] B. Daraby and L. Arabi, Related Fritz Carlson type inequality for Sugeno integrals, Soft Comput., 17 (2013), pp. 1745-1750.
14
[15] B. Daraby and F. Ghadimi, General Minkowsky type and related inequalities for seminormed fuzzy integrals, Sahand Commun. Math. Anal., 1(1) (2014), pp. 9-20.
15
[16] B Daraby, A. Shafiloo and A. Rahimi, Geberalizations of the Feng Qi type inequality for Pseudo-integral, Gazi University Journal of Science, 28(4) (2015), pp. 695-702.
16
[17] B. Daraby, F. Rostampour and A. Rahimi, Hardy's Type Inequality For Pseudo-Integrals, Acta Univ. Apulensis, Math. Inform., 42 (2015), pp. 53-65
17
[18] B. Daraby, H. Ghazanfary Asll and I. Sadeqi, Favard’s inequality for seminormed fuzzy integral and semiconormed fuzzy integral, Mathematica, 58 (81) (2016), pp. 39–50.
18
[19] B. Daraby, A Convolution Type Inequality For pseudo-Integrals, Acta Univ. Apulensis, Math. Inform., 48 (2016), pp. 27-35.
19
[20] B. Daraby, Results Of The Chebyshev Type Inequality For Pseudo-Integral, Sahand Commun. Math. Anal., 4 (1) (2016), [pp.] 91-100.
20
[21] B. Daraby and A. Rahimi, Jensen type inequality for seminormed fuzzy integrals, Acta Univ. Apulensis, Math. Inform., 46 (2016), pp. 1-8.
21
[22] B. Daraby, H. Ghazanfary Asll and I. Sadeqi, General related inequalities to Carlson-type inequality for the Sugeno integral, Appl. Math. Comput., 305 (2017), pp. 323-329.
22
[23] B. Daraby, Generalizations of the Well-Known Chebyshev Type Inequalities for Pseudo-Integrals, Gen. Math. Notes, 38 (1) (2017), pp. 32-45.
23
[24] B. Daraby, H. Ghazanfary Asll and I. Sadeqi, General related inequalities to Carlson-type inequality for the Sugeno integral, Appl. Math. Comput., 305 (15) (2017), pp. 323-329.
24
[25] B. Daraby, A, Shafiloo and A. rahimi, Carlson Type Inequality For Choquet-Like Expectation, Acta Univ. Apulensis, Math. Inform., 49 (2017), pp. 23-36.
25
[26] B. Daraby, H. Ghazanfary Asll and I. Sadeqi, Gronwall's Inequality For Pseudo-Integral, An. Univ. Oradea, Fasc. Mat., XXIV (1) (2017), pp. 67-74.
26
[27] B. Daraby, F. Rostampour and A. Rahimi, Minkowski type inequality for fuzzy and pseudo-integrals, Tbil. Math. J., 10 (2) (2017), pp. 243-258.
27
[28] B. Daraby, A. Shafiloo and A. Rahimi, General Lyapunov type inequality for Sugeno integral, J. Adv. Math. Stud., 11 (1) (2018), pp. 37-46.
28
[29] B. Daraby, F. Rostampour and A. Rahimi, Minkowski type inequality for fuzzy and pseudo-integrals, Tibilis Mathematical Journal., 10 (4) (2017), pp. 159-174.
29
[30] B. Daraby, H. Ghazanfary Asll and I. Sadeqi, General related inequalities to Carlson-type inequality for the Sugeno integral, Appl. Math. Comput., 305 (15) (2017), pp. 323-329.
30
[31] B. Daraby, General Related Jensen type Inequalities for fuzzy integrals, TWMS J. Pure Appl. Math., 8 (1) (2018), pp. 1-7.
31
[32] B. Daraby, H. Ghazanfary Asll and I. Sadeqi, Favard’s inequality for pseudo-integral, Asian-Eur. J. Math., 11 (1) (2018)
32
[33] B. Daraby, F. Rostampour, A.R. Khodadadi and A. Rahimi, Related Gauss-Winkler Type Inequality for Fuzzy and Pseudo-Integrals, Thai J. Math., 19 (2) (2021), pp. 713-724.
33
[34] B. Daraby, R. Mesiar, F. Rostampour and A. Rahimi, Related Thunsdorff type and FrankPick type inequalities for Sugeno integral, Appl. Math. Comput., 414 (2022).
34
[35] B. Daraby, R. Mesiar, F. Rostampour and A. Rahimi, Related Thunsdorff type and Frank-P-ck type inequalities for Sugeno integral, Appl. Math. Comput., 414: 126683 (2022).
35
[36] B. Daraby, F. Rostampour, A.R. Khodadadi, A. Rahimi and R. Mesiar, Polya-Knopp and Hardy-Knopp type inequalities for Sugeno integral, arXiv:1910.03812v1.
36
[37] A. Flores-Franulic and H. Roman-Flores, A Chebyshev type inequality for fuzzy integrals, Appl. Math. Comput., 190 (2007), pp. 1178-1184.
37
[38] A. Flores-Franulic, H. Roman-Flores and Y. Chalco-Cano, A note on fuzzy integral inequality of Stolarsky type, Appl. Math. Comput., 196 (2008), pp. 55-59.
38
[39] L. Gajek and A. Okolewski, Steffensen type inequalities for order and record statistics, Ann. Univ. Mariae Curie-Skaodowska Lublin-Polonia, 16 (1997), pp. 41-59.
39
[40] R.J. Gardner, The Brunn-Minkowski inequality, Bull. Am. Math. Soc., 39 (2002), pp. 355-405.
40
[41] I. Gentil, From the Prekopa-Leindler inequality to modified logarithmic Sobolev inequality, Ann. Fac. Sci. Toulouse, Math., 17 (2) (2008), pp. 291-308.
41
[42] D.H. Hong, Gauss-Winikler inequality for Sugeno integrals, Int. J. Pure Appl. Math., 116 (2) (2017), pp. 479-487.
42
[43] J.Y. Lu , K.S. Wu and J.C. Lin, Fast full search in motion estimation by hierarchical use of Minkowski's inequality, Pattern Recognition, 31 (1998), pp. 945-952.
43
[44] R. Mesiar and Y. Ouyang, General Chebyshev type inequalities for Sugeno integrals, Fuzzy Sets Syst., 160 (2009), pp. 58-64.
44
[45] H. Minkowski, Geometrie der Zahlen, Teubner, Leipzig, 1910.
45
[46] Y. Ouyang, J. Fang and L. Wang, Fuzzy Chebyshev type inequality, Internatinal Journal of Approximate Reasoning, 48 (2008), pp. 829-835.
46
[47] U.M. Ozkan, M.Z. Sarikaya and H. Yildirim, Extensions of certain integral inequalities on time scales, Appl. Math. Lett., 21 (2008), pp. 993-1000.
47
[48] E. Pap, Null-additive Set Functions, Kluwer, Dordrecht, 1995.
48
[49] A. Prekopa, Stochastic Programming, Kluwer, Dordretch, 1995.
49
[50] D. Ralescu and G. Adams, The fuzzy integral, J. Appl. Math. Anal. Appl., 75 (1980), pp. 562-570.
50
[51] H. Roman-Flores, A. Flores-Franulic and Y. Chalco-Cano, The fuzzy integral for monotone functions, Appl. Math. Comput., 185 (2007), pp. 492-498.
51
[52] H. Roman-Flores and Y. Chalco-Cano, Sugeno integral and geometric inequalities, International Journal of Uncertainity, Fuzziness and Knowledge-Based Systtem, 15 (2007), pp. 1-11.
52
[53] H. Roman-Flores, A. Flores-Franulic and Y. Chalco-Cano, A Jensen type inequality for fuzzy integrals, Inf. Sci., 177 (2007), pp. 3192-3201.
53
[54] H. Roman-Flores, A. Flores-Franulic and Y. Chalco-Cano, A convolution type inequality for fuzzy integrals, Appl. Math. Comput., 195 (2008), pp. 94-99.
54
[55] H. Roman-Flores, A. Flores-Franulic and Y. Chalco-Cano, A note on fuzzy integral inequality of Stolarsky type, Appl. Math. Comput., 196 (2008), pp. 55-59.
55
[56] H. Roman-Flores, A. Flores-Franulic and Y. Chalco-Cano, A Hardy-type inequality for fuzzy integrals, Appl. Math. Comput., 204 (2008), pp. 178-183.
56
[57] W. Rudin, Principles of Mathematical Analysis, 3rd Edition, McGraw-Hill, New York, 1976.
57
[58] W. Rudin, Real and Complex Analysis, 3rd Edition, McGraw-Hill, New York, 1987.
58
[59] H. Roman-Flores, A. Flores-Franulic and Y. Chalco-Cano, A Hardy-type inequality for fuzzy integrals, Appl. Math. Comput., 204 (2008), pp. 178-183.
59
[60] I. Sadeqi, H. Ghazanfary Asll and B. Daraby, Gauss type inequality for Sugeno integral, J. Adv. Math. Stud., 10 (2) (2017), pp. 167-173.
60
[61] R. Srivastava, Some families of integral, trigonometric and other related inequalities, Appl. Math. Inf. Sci., 5 (2011), pp. 342-360.
61
[62] M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. thesis, Tokyo Institute of Technology, 1974.
62
[63] Z. Wang and G. Klir, Fuzzy Measure Theory, Plenum Press, New York, 1992.
63