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

Choonkil Park; Abbas Najati; Batool Noori; Mohammad B. Moghimi; Choonkil Park; Abbas Najati; Batool Noori; Mohammad B. Moghimi

doi:10.3934/math.2022188

AIMS Mathematics

2022, Volume 7, Issue 3: 3379-3394. doi: 10.3934/math.2022188

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Research article

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

1.
Department of Mathematics, Hanyang University, Korea
2.
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran

Received: 16 September 2021 Accepted: 11 November 2021 Published: 30 November 2021
MSC : 39B82, 39B52, 39B62, 46C15

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.
- Hyers-Ulam stability,
- quadratic functional equation,
- Fréchet functional equation,
- asymptotic behavior
Citation: Choonkil Park, Abbas Najati, Batool Noori, Mohammad B. Moghimi. Additive and Fréchet functional equations on restricted domains with some characterizations of inner product spaces[J]. AIMS Mathematics, 2022, 7(3): 3379-3394. doi: 10.3934/math.2022188

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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.

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