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Research Article | Open Access

Approximate solution of a multivariable Cauchy-Jensen functional equation

Jae-Hyeong Bae1, Won-Gil Park2( )
Humanitas College, Kyung Hee University, Yongin 17104, Republic of Korea
Department of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, Republic of Korea
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Abstract

Let n be an integer greater than 1. In this paper, we obtained the stability of the multivariable Cauchy-Jensen functional equation

n f ( x 1 + ⋯ + x n , y 1 + ⋯ + y n n ) = ∑ 1 ≤ i , j ≤ n f ( x i , y j )

in Banach spaces, quasi-Banach spaces, and normed 2-Banach spaces.

Keywords

linear 2-normed spacequasi-normed spaceCauchy-Jensen mapping
CLC number: 39B52, 39B82

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AIMS Mathematics
Volume 9 Issue 3,
March 2024
Pages 7084-7094
DOI: 10.3934/math.2024345

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Cite this article:
Bae J-H, Park W-G. Approximate solution of a multivariable Cauchy-Jensen functional equation. AIMS Mathematics, 2024, 9(3): 7084-7094. https://doi.org/10.3934/math.2024345

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Received: 15 December 2023
Revised: 26 January 2024
Accepted: 01 February 2024
Published: 15 March 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)