The Stability of the Generalized Function Equation (European Journal of Pure and Applied Mathematics, 2025)
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 nonemptyset $S $ such that $\sup\{|\alpha(x)| : x\in S\} < 1$ and $f_i(x) (i=1,2)$ are given mappings.