Fixed Point Theory and the Ulam Stability

Abstract EN

The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable.

However, most authors follow the approaches involving a theorem of Diaz and Margolis.

The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940.