The Stability of the Generalized Function Equation
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i3.6197Keywords:
functional inequations, Hyers-Ulam stability, Banach space.Abstract
The aim of this paper is to prove the stability (in the sense of Ulam)
of the functional equation:
\begin{eqnarray*}
f(x)=\alpha(x)f(f_1(x))+\beta(x)f(f_2(x)),
\end{eqnarray*}
where $\alpha$ and $\beta$ are given real valued functions defined on a nonempty
set $S $ such that $\sup\{|\alpha(x)| : x\in S\} < 1$ and $f_i(x) (i=1,2)$ are given mappings.
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Copyright (c) 2025 Gang Lyu, Yingxiu Jiang, Qi Liu, Choonkil Park
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