Fixed Point Theory and the Ulam Stability. (13th August 2014)

• Record Type: Journal Article
• Authors: Brzdęk, Janusz; Cădariu, Liviu; Ciepliński, Krzysztof
• Other Names: Leśniak Zbigniew Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-08-13
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/829419
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.