(untitled) (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: 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 nonempty set S such that {|α(x)| : xS} < 1 and f_i(x) (i=1,2) are given mappings.