Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 3, Number 1 (2012), 151-164.
Applications of fixed point theorems to the Hyers-Ulam stability of functional equations–a survey
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.
Ann. Funct. Anal., Volume 3, Number 1 (2012), 151-164.
First available in Project Euclid: 12 May 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 39B82: Stability, separation, extension, and related topics [See also 46A22]
Secondary: 47H10 46S10
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