Open AccessAdditive and Fréchet functional equations on restricted domains with some characterizations of inner product spaces
Author(s) -
Choonkil Park,
Abbas Najati,
Batool Noori,
M. B. Moghimi
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022188
Subject(s) - mathematics , product (mathematics) , stability (learning theory) , pure mathematics , functional equation , inner product space , functional analysis , mathematical analysis , computer science , chemistry , geometry , differential equation , biochemistry , machine learning , gene
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.