Open Access

Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces

Fixed Point Theory and Applications20092009:589143

https://doi.org/10.1155/2009/589143

Received: 24 April 2009

Accepted: 19 October 2009

Published: 22 November 2009

Abstract

We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations (linear functional equations, generalized equation of the square root, spiral generalized gamma equations) in random normed spaces. As direct and natural consequences of our results, we obtain general stability properties for the corresponding functional equations in (deterministic) metric and normed spaces.

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Authors’ Affiliations

(1)
Department of Mathematics, "Politehnica" University of Timişoara
(2)
Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara

Copyright

© L. Cădariu and V. Radu. 2009

This article is published under license to BioMed Central Ltd. 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.