Approximation of almost quadratic mappings via modular functional

Volume 29, Issue 2, pp 106--117 http://dx.doi.org/10.22436/jmcs.029.02.01

Publication Date: August 24, 2022 Submission Date: February 09, 2022 Revision Date: July 01, 2022 Accteptance Date: July 07, 2022

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Authors

I.-S. Chang - Department of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon 34134, Korea. H.-M. Kim - Department of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon 34134, Korea. H.-W. Lee - Department of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon 34134, Korea.

Abstract

In this paper, we present generalized stability results of refined quadratic functional equation \[ f(ax-by)=abf(x-y)+a(a-b)f(x)+b(b-a)f(y), \] for any fixed nonzero integer numbers \(a,b\in\mathbb{Z}\) with \(a\neq b\) in modular spaces. As results, we generalize stability results of a quadratic functional equation in [{K.-W. Jun, H.-M. Kim, J. Son, Functional Equations in Mathematical Analysis, \(\bf{2012}\) (2012), 153--164}].

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Keywords

• Generalized Hyers-Ulam stability
• modular functional
• modular spaces

MSC

•  39B82
•  39B72
•  16W25

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