Asymptotic behavior of Fréchet functional equation and some characterizations of inner product spacesopen access
- Authors
- Park, Choonkil; Tareeghee, Mohammad Amin; Najati, Abbas; Yengejeh, Yavar Khedmati; Paokanta, Siriluk
- Issue Date
- Oct-2023
- Publisher
- DE GRUYTER POLAND SP Z O O
- Keywords
- Hyers-Ulam stability; quadratic function; cubic function; Frechet functional equation; asymptotic behavior
- Citation
- DEMONSTRATIO MATHEMATICA, v.56, no.1, pp.1 - 13
- Indexed
- SCIE
SCOPUS
- Journal Title
- DEMONSTRATIO MATHEMATICA
- Volume
- 56
- Number
- 1
- Start Page
- 1
- End Page
- 13
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/192884
- DOI
- 10.1515/dema-2023-0265
- ISSN
- 0420-1213
- Abstract
- This article presents the general solution f : G -> V of the following functional equation: f(x) - 4f(x + y) + 6f(x + 2y) - 4f(x + 3y) + f(x + 4y) = 0, x,y is an element of g,where (G, +) is an abelian group and N is a linear space. We also investigate its Hyers-Ulam stability on some restricted domains. We apply the obtained results to present some asymptotic behaviors of this functional equation in the framework of normed spaces. Finally, we provide some characterizations of inner product spaces associated with the mentioned functional equation.
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