×

An application of Banach’s fixed point theorem to the stability of a general functional equation. (English) Zbl 1240.39058

Summary: Using the Banach fixed point theorem, we establish the stability of the functional equation \(f(z)=G(f(z),f(\varphi (z)))\), where \(f\) is an unknown function, under certain natural assumptions on functions \(G\) and \(\varphi\). Our main result slightly extends a known one of J. Baker.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
PDFBibTeX XMLCite