Approximate solution of a multivariable Cauchy-Jensen functional equation

Jae-Hyeong Bae; Won-Gil Park; Jae-Hyeong Bae; Won-Gil Park

doi:10.3934/math.2024345

AIMS Mathematics

2024, Volume 9, Issue 3: 7084-7094. doi: 10.3934/math.2024345

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Research article

Approximate solution of a multivariable Cauchy-Jensen functional equation

Jae-Hyeong Bae ¹,
Won-Gil Park ^{2
,
,}

1.
Humanitas College, Kyung Hee University, Yongin 17104, Republic of Korea
2.
Department of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, Republic of Korea

Received: 15 December 2023 Revised: 26 January 2024 Accepted: 01 February 2024 Published: 19 February 2024
MSC : 39B52, 39B82

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

$ nf\bigg(x_1+{\cdots}+x_n, \frac {y_1+{\cdots}+y_n}n\bigg) = \sum\limits_{1\le i, j\le n}f(x_i, y_j) $

in Banach spaces, quasi-Banach spaces, and normed $ 2 $-Banach spaces.
- linear $ 2 $-normed space,
- quasi-normed space,
- Cauchy-Jensen mapping
Citation: Jae-Hyeong Bae, Won-Gil Park. Approximate solution of a multivariable Cauchy-Jensen functional equation[J]. AIMS Mathematics, 2024, 9(3): 7084-7094. doi: 10.3934/math.2024345

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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

$ nf\bigg(x_1+{\cdots}+x_n, \frac {y_1+{\cdots}+y_n}n\bigg) = \sum\limits_{1\le i, j\le n}f(x_i, y_j) $

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

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