A Fixed Point Approach to the Hyers-Ulam-Rassias Stability Problem of Pexiderized Functional Equation in Modular Spaces-Reference-Cited by-同舟云学术

A Fixed Point Approach to the Hyers-Ulam-Rassias Stability Problem of Pexiderized Functional Equation in Modular Spaces

Published:2021-10-01 Issue:1 Volume:78 Page:59-72
ISSN:1338-9750
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Saha Parbati¹,Mondal Pratap²,Chqudhury Binayak S.¹

Affiliation:

1. 1 Department of Mathematics , Indian Institute of Engineering Science and Technology , Shibpur, Howrah, West Bengal , INDIA

2. 2 Department of Mathematics , Bijoy Krishna Girls’ College , Howrah, West Bengal , INDIA

Abstract

Abstract In this paper, we consider pexiderized functional equations for studying their Hyers-Ulam-Rassias stability. This stability has been studied for a variety of mathematical structures. Our framework of discussion is a modular space. We adopt a fixed-point approach to the problem in which we use a generalized contraction mapping principle in modular spaces. The result is illustrated with an example.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2021-0005

Reference45 articles.

1. [1] ABDOU, A.A.N.—KHAMSI, M.A.: Fixed point theorems in modular vector spaces, J. Nonlinear Sci. Appl. 10 (2017), 4046–4057.10.22436/jnsa.010.08.01

2. [2] GRABIEC, A.: The generalized Hyers-Ulam stability of a class of functional equations, Publ. Math. Debrecen 48 (1996), 217–235.10.5486/PMD.1996.1559

3. [3] MIRMOSTAFAEE, V.—MOSLEHIAN, M. S.: Stability of additive mappings in non-Archimedean fuzzy normed spaces, Fuzzy Sets and 5ystems 160 (2009), 1643–1652.10.1016/j.fss.2008.10.011

4. [4] KIM, C.—PARK, S.W.: A Fixed point approach to the stability of additive-quadratic functional equations in modular spaces, J. of The Chungcheong Math. Soc. 18 (2015), 321–330.10.14403/jcms.2015.28.2.321

5. [5] HYERS, D. H.: On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222–224.10.1073/pnas.27.4.222107831016578012