Fixed points of a mapping and Hyers-Ulam stability

We show that many general results on Hyers-Ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem. The theorem is formulated for self-maps of some subsets of the space of functions from a nonempty set into the set of reals. We also give some applications of that theorem, e.g., in investigations of solutions of some difference equations and functional inequalities. (C) 2013 Elsevier Inc, All rights reserved;