A fixed point approach to the stability of functional equations in non-Archimedean metric spaces

In this note, we prove a simple fixed point theorem for a special class of complete metric spaces (namely, complete non-Archimedean metric spaces which are connected with some problems coming from quantum physics, pp-adic strings and superstrings). We also show that this theorem is a very efficient and convenient tool for proving the Hyers–Ulam stability of a quite wide class of functional equations in a single variable.