AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVE  -FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS*

doi:10.1007/s10473-024-0117-z

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (1): 311-338.doi: 10.1007/s10473-024-0117-z

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVE -FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS^*

Safoura Rezaei Aderyani¹, Azam Ahadi¹, Reza Saadati^1,†, Hari M. Srivastava^2,3,4,5

1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran;
2. Department of Mathematics and Statistics, Universtity of Victoria, Canada;
3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, China;
4. Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan;
5. Section of Mathematics, International Telematic, University Uninettuno, I-00186 Rome, Italy

收稿日期:2022-08-04 修回日期:2023-03-17 出版日期:2024-02-25 发布日期:2024-02-27
通讯作者: † Reza Saadati1, E-mail: rsaadati@eml.cc
作者简介:Safoura Rezaei Aderyani, E-mail: safora.rezaei.2000@gmail.com; Azam Ahadi, azamahadi9710@gmail.com; Hari M. Srivastava, E-mail: harimsri@math.uvic.ca
基金资助:
Natural Sciences and Engineering Research Council of Canada (2019-03907).

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVE -FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS^*

Safoura Rezaei Aderyani¹, Azam Ahadi¹, Reza Saadati^1,†, Hari M. Srivastava^2,3,4,5

1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran;
2. Department of Mathematics and Statistics, Universtity of Victoria, Canada;
3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, China;
4. Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan;
5. Section of Mathematics, International Telematic, University Uninettuno, I-00186 Rome, Italy

Received:2022-08-04 Revised:2023-03-17 Online:2024-02-25 Published:2024-02-27
Contact: † Reza Saadati1, E-mail: rsaadati@eml.cc
About author:Safoura Rezaei Aderyani, E-mail: safora.rezaei.2000@gmail.com; Azam Ahadi, azamahadi9710@gmail.com; Hari M. Srivastava, E-mail: harimsri@math.uvic.ca
Supported by:
Natural Sciences and Engineering Research Council of Canada (2019-03907).

摘要/Abstract

摘要： In this paper, we define a new class of control functions through aggregate special functions. These class of control functions help us to stabilize and approximate a tri-additive $\boldsymbol{\psi}$-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital $C^*$-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

关键词: permuting tri-homomorphism in Banach algebra, permuting tri-derivation on $C^*$-algebra, fixed point theorem, Ulam-Hyers-Rassias stability, aggregate special functions, tri-additive $\boldsymbol{\psi}$-functional inequality

Abstract: In this paper, we define a new class of control functions through aggregate special functions. These class of control functions help us to stabilize and approximate a tri-additive $\boldsymbol{\psi}$-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital $C^*$-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

Key words: permuting tri-homomorphism in Banach algebra, permuting tri-derivation on $C^*$-algebra, fixed point theorem, Ulam-Hyers-Rassias stability, aggregate special functions, tri-additive $\boldsymbol{\psi}$-functional inequality

中图分类号:

39B52

Safoura Rezaei Aderyani, Azam Ahadi, Reza Saadati, Hari M. Srivastava. AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVE -FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS^*[J]. 数学物理学报(英文版), 2024, 44(1): 311-338.

参考文献

[1] Grabisch M, Marichal J L, Mesiar R, Pap E. Aggregation Functions.Cambridge: Cambridge University Press, 2009
[2] Luo Y, Zhu K. Characterizations for the cross-migrativity between overlap functions and commutative aggregation functions. Information Sciences, 2023, 622: 303-318
[3] Candeal J C. Abstract aggregation functions and social choice. Fuzzy Sets and Systems, 2023, 454: 190-198
[4] Debnath K, Roy S K. Power partitioned neutral aggregation operators for T-spherical fuzzy sets: An application to H2 refuelling site selection. Expert Systems with Applications, 2023, 216: 119470
[5] Aderyani S R, Saadati R. Best approximations of the $ \phi$-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions. Adv Differ Equ, 2021, 2021(1): Art 154
[6] Karthikeyan S, Park C, Palani P, Kumar T R K. Stability of an additive-quartic functional equation in modular spaces. J Math Computer Sci, 2022, 26(1): 22-40
[7] Park C, Jin Y, Shin D, Zhang X, Govindan V. Permuting triderivations and permuting trihomomorphisms in Banach algebras. Rocky Mountain J Math, 2020, 50(5): 1793-1806
[8] Aderyani S R, Saadati R, Mesiar R. Estimation of permuting tri-homomorphisms and permuting tri-derivations associated with the tri-additive $\Upsilon$-random operator inequality in matrix MB-algebra. International Journal of General Systems, 2022, 51(6): 547-569
[9] Aderyani S R, Saadati R, O'Regan D, Alshammari F S. Multi-super-stability of antiderivations in Banach algebras. AIMS Mathematics, 2022, 7(11): 20143-20163
[10] Aderyani S R, Saadati R, O'Regan D, Alshammari F S. Existence, uniqueness and stability analysis with the multiple Exp function method for NPDEs. Mathematics, 2022, 10(21): Art 4151
[11] Diaz J B, Margolis B. A fixed point theorem of the alternative, for contractions on a generalized complete metric space. Bull Am Math Soc, 1968, 74: 305-309
[12] Bonforte M, Endal J. Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions,functional inequalities. Journal of Functional Analysis, 2023, 284(6): 109831
[13] Van An L. Generalized stability of functional inequalities with 3k-variables associated for Jordan-von Neumann-type additive functional equation. Open Access Library Journal, 2023, 10(1): 1-17
[14] Kopfer E, Streets J. Bochner formulas, functional inequalities and generalized Ricci flow. Journal of Functional Analysis, 2023, 284(10): Art 109901
[15] Van An L. Generalized stability additive $ \lambda$-functional inequalities with 3k-variable in $ \alpha$-homogeneous F-spaces. International Journal of Analysis and Applications, 2022, 20: 43-43
[16] Bae J, Park W. Approximate bi-homomorphisms and bi-derivations in $C^*$-ternary algebras. Bull Korean Math Soc, 2010, 47: 195-209

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVE -FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS^*

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVE -FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS^*

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	蒋宜蓉, 魏周超, 卢景苹. THE NONEMPTINESS AND COMPACTNESS OF MILD SOLUTION SETS FOR RIEMANN-LIOUVILLE FRACTIONAL DELAY DIFFERENTIAL VARIATIONAL INEQUALITIES[J]. 数学物理学报(英文版), 2021, 41(5): 1569-1578.
[2]	Bashir AHMAD, Ravi P. AGARWAL, Abrar BROOM, Ahmed ALSAEDI. ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS[J]. 数学物理学报(英文版), 2021, 41(4): 1366-1384.
[3]	翁云华, 李雪松, 黄南京. A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES[J]. 数学物理学报(英文版), 2021, 41(1): 187-206.
[4]	Laddawan AIEMSOMBOON, Wutiphol SINTUNAVARAT. ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES[J]. 数学物理学报(英文版), 2020, 40(3): 824-834.
[5]	郭铁信, 张二鑫, 王亚超, 袁先智. $L^0$-CONVEX COMPACTNESS AND RANDOM NORMAL STRUCTURE IN $L^0(\mathcal{F},B)$[J]. 数学物理学报(英文版), 2020, 40(2): 457-469.
[6]	蒲学科, 郭柏灵. INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL[J]. 数学物理学报(英文版), 2020, 40(2): 529-542.
[7]	Syed Sabyel HAIDER, Mujeeb Ur REHMAN. ULAM-HYERS-RASSIAS STABILITY AND EXISTENCE OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENCE EQUATIONS WITH MULTIPOINT SUMMATION BOUNDARY CONDITION[J]. 数学物理学报(英文版), 2020, 40(2): 589-602.
[8]	A. BEN MAKHLOUF, D. BOUCENNA, M. A. HAMMAMI. EXISTENCE AND STABILITY RESULTS FOR GENERALIZED FRACTIONAL DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2020, 40(1): 141-154.
[9]	Iz-iddine EL-FASSI, Hamid KHODAEI, Themistocles M. RASSIAS. APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES[J]. 数学物理学报(英文版), 2019, 39(2): 369-381.
[10]	梁载涛, 杨艳娟. RADIAL CONVEX SOLUTIONS OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE[J]. 数学物理学报(英文版), 2019, 39(2): 395-402.
[11]	Janusz BRZDȨK, Krzysztof CIEPLINSKI. ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS[J]. 数学物理学报(英文版), 2018, 38(2): 377-390.
[12]	宋威, 李林. CONTINUOUSLY DECREASING SOLUTIONS FOR A GENERAL ITERATIVE EQUATION[J]. 数学物理学报(英文版), 2018, 38(1): 177-186.
[13]	Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ. ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION[J]. 数学物理学报(英文版), 2017, 37(6): 1727-1739.
[14]	Bashir AHMAD, Sotiris K. NTOUYAS, Jessada TARIBOON. A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2016, 36(6): 1631-1640.
[15]	刘玉记. PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS[J]. 数学物理学报(英文版), 2016, 36(5): 1492-1508.