Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 589143, 18 pages
doi:10.1155/2009/589143
Research Article

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

Liviu Cădariu1 and Viorel Radu2

1Department of Mathematics, “Politehnica” University of Timişoara, Piaţa Victoriei number 2, 300006 Timişoara, Romania
2Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, Vasile Pârvan 4, 300223 Timişoara, Romania

Received 24 April 2009; Accepted 19 October 2009

Academic Editor: Tomas Dominguez Benavides

Copyright © 2009 Liviu Cădariu and Viorel Radu. 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

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.