Fixed Point Theory and the Ulam Stability

By Janusz Brzdek, Liviu Cadariu, Krzysztof Cieplinski. 2014

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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.

Subfields: Applied Mathematics

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