Applications of fixed point theorems to the Hyers-Ulam stability‎ ‎of functional equations–a survey

Abstract

‎The fixed point method‎, ‎which is the second most popular technique‎ ‎of proving the Hyers-Ulam stability of functional equations‎, ‎was‎ ‎used for the first time in 1991 by J.A‎. ‎Baker who applied a variant‎ ‎of Banach's fixed point theorem to obtain the stability of a‎ ‎functional equation in a single variable‎. ‎However‎, ‎most authors‎ ‎follow Radu's approach and make use of 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 the Hyers-Ulam‎ ‎stability of functional equations‎.