Annals of Functional Analysis

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

Krzysztof Ciepliński

Full-text: Open access

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.

Article information

Source
Ann. Funct. Anal. Volume 3, Number 1 (2012), 151-164.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399900032

Digital Object Identifier
doi:10.15352/afa/1399900032

Mathematical Reviews number (MathSciNet)
MR2903276

Zentralblatt MATH identifier
1252.39032

Subjects
Primary: 39B82: Stability, separation, extension, and related topics [See also 46A22]
Secondary: 47H10‎ ‎46S10

Keywords
Hyers-Ulam stability ‎functional equation ‎fixed point‎ ‎theorem ‎ultrametric

Citation

Ciepliński, Krzysztof. Applications of fixed point theorems to the Hyers-Ulam stability‎ ‎of functional equations–a survey. Ann. Funct. Anal. 3 (2012), no. 1, 151--164. doi:10.15352/afa/1399900032. https://projecteuclid.org/euclid.afa/1399900032


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