Mathematical analysis confirms stability of a functional equation involving mappings, suggesting broader applications.
The aim of this paper is to prove the stability (in the sense of Ulam)of the functional equation:{eqnarray*}f(x)=α(x)f(f_1(x))+β(x)f(f_2(x)),{eqnarray*}where α and β are given real valued functions defined on a nonemptyset S such that \|α(x)| : x∈ S\ < 1 and fᵢ(x) (i=1,2) are given mappings.
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Lyu et al. (2025) studied this question.
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