Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces

被引：4

作者：

Tamilvanan, Kandhasamy ^{[1
]}

Alkhaldi, Ali H. ^{[2
]}

Jakhar, Jyotsana ^{[3
]}

Chugh, Renu ^{[3
]}

Jakhar, Jagjeet ^{[4
]}

Rassias, John Michael ^{[5
]}

机构：

[1] RMK Engn Coll, Dept Math, Fac Sci & Humanities, Tiruvallur 601206, Tamil Nadu, India

[2] King Khalid Univ, Coll Sci, Dept Math, Abha 61421, Saudi Arabia

[3] Maharshi Dayanand Univ, Dept Math, Rohtak 124001, Haryana, India

[4] Cent Univ Haryana, Dept Math, Mahendergarh 123031, Haryana, India

[5] Natl & Kapodistrian Univ Athens, Pedag Dept Math & Informat, Attikis 15342, Greece

来源：

MATHEMATICS | 2023年 / 11卷 / 02期

关键词：

quartic and quintic functional equations; modular spaces; 2-Banach spaces; refined stability; RASSIAS STABILITY; HYERS;

D O I：

10.3390/math11020371

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we investigate the refined stability of the additive, quartic, and quintic functional equations in modular spaces with and without the & UDelta;2-condition using the direct method (Hyers method). We also examine Ulam stability in 2-Banach space using the direct method. Additionally, using a suitable counterexample, we eventually demonstrate that the stability of these equations fails in a certain case.

引用

页数：23

共 50 条

[21] Stability Property of Functional Equations in Modular Spaces: A Fixed-Point Approach
P. Saha
Pratap Mondal
B. S. Choudhury
Mathematical Notes, 2021, 109 : 262 - 269
[22] UNIQUENESS THEOREM CONCERNING FUNCTIONAL EQUATIONS IN MODULAR SPACES
Jeon, Youngju
Kim, Changil
JOURNAL OF APPLIED MATHEMATICS & INFORMATICS, 2020, 38 (5-6): : 415 - 426
[23] Generalized Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces
Rassias, John Michael
Kim, Hark-Mahn
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 356 (01) : 302 - 309
[24] On Ulam Stability of a Functional Equation in Banach Modules
Oubbi, Lahbib
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2017, 60 (01): : 173 - 183
[25] Ulam's-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi-Banach Spaces
Wang, JinRong
Zada, Akbar
Ali, Wajid
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2018, 19 (05) : 553 - 560
[26] Lipschitz stability of operators in Banach spaces
V. Yu. Protasov
Proceedings of the Steklov Institute of Mathematics, 2013, 280 : 268 - 279
[27] A Remark for the Hyers-Ulam Stabilities on n-Banach Spaces
Choy, Jaeyoo
Chu, Hahng-Yun
Kim, Ahyoung
AXIOMS, 2021, 10 (01) : 1 - 10
[28] On the general solution of a quadratic functional equation and its Ulam stability in various abstract spaces
Shen, Yonghong
Lan, Yaoyao
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2014, 7 (06): : 368 - 378
[29] Y Stability of an additive-quartic functional equation in modular spaces
Karthikeyan, S.
Park, Choonkil
Palani, P.
Kumar, T. R. K.
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2020, 26 (01): : 22 - 40
[30] Generalized Hyers-Ulam Stability of n-Dimensional Quadratic Functional Equality in Modular Space and β-Homogeneous Banach Space
Baza, A.
Rossafi, M.
AZERBAIJAN JOURNAL OF MATHEMATICS, 2025, 15 (01): : 25 - 43

← 1 2 3 4 5 →