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The Stability of the Generalized Functional Equation
- Authors
- Lyu, Gang; Jiang, Yingxiu; Liu, Qi; Park, Choonkil
- Issue Date
- Jul-2025
- Publisher
- New York Business Global
- Keywords
- Functional inequations; Hyers-Ulam stability; Banach space
- Citation
- European Journal of Pure and Applied Mathematics, v.18, no.3, pp 1 - 17
- Pages
- 17
- Indexed
- SCOPUS
ESCI
- Journal Title
- European Journal of Pure and Applied Mathematics
- Volume
- 18
- Number
- 3
- Start Page
- 1
- End Page
- 17
- ISSN
- 1307-5543
1307-5543
- Abstract
- The aim of this paper is to prove the stability (in the sense of Ulam) of the functional equation: f(x) = alpha(x)f(f(1)(x)) + beta(x)f(f(2)(x)), where alpha and beta are given real valued functions defined on a nonempty set S such that sup{|alpha(x)| : x is an element of S} < 1 and f(i)(x)(i = 1, 2) are given mappings.
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