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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 712743, 10 pages
http://dx.doi.org/10.1155/2012/712743
Research Article

Fixed Points and Generalized Hyers-Ulam Stability

Department of Mathematics, “Politehnica” University of Timişoara, Piaţa Victoriei No. 2, 300006 Timişoara, Romania

Received 17 May 2012; Accepted 5 July 2012

Academic Editor: Krzysztof Ciepliński

Copyright © 2012 L. Cădariu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we prove a fixed-point theorem for a class of operators with suitable properties, in very general conditions. Also, we show that some recent fixed-points results in Brzdęk et al., (2011) and Brzdęk and Ciepliński (2011) can be obtained directly from our theorem. Moreover, an affirmative answer to the open problem of Brzdęk and Ciepliński (2011) is given. Several corollaries, obtained directly from our main result, show that this is a useful tool for proving properties of generalized Hyers-Ulam stability for some functional equations in a single variable.