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Research Article | Open Access

Additive and Fréchet functional equations on restricted domains with some characterizations of inner product spaces

Choonkil Park1, Abbas Najati2( ), Batool Noori2, Mohammad B. Moghimi2( )
Department of Mathematics, Hanyang University, Korea
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
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Abstract

In this paper, we investigate the Hyers-Ulam stability of additive and Fréchet functional equations on restricted domains. We improve the bounds and thus the results obtained by S. M. Jung and J. M. Rassias. As a consequence, we obtain asymptotic behaviors of functional equations of different types. One of the objectives of this paper is to bring out the involvement of functional equations in various characterizations of inner product spaces.

Keywords

Hyers-Ulam stabilityquadratic functional equationFréchet functional equationasymptotic behavior
CLC number: 39B82, 39B52, 39B62, 46C15

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 3379-3394
DOI: 10.3934/math.2022188

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Cite this article:
Park C, Najati A, Noori B, et al. Additive and Fréchet functional equations on restricted domains with some characterizations of inner product spaces. AIMS Mathematics, 2022, 7(3): 3379-3394. https://doi.org/10.3934/math.2022188

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Received: 16 September 2021
Accepted: 11 November 2021
Published: 15 March 2021
©2022 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)