doi:10.1155/2009/589143 Research Article Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces

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. Copyright q 2009 L. Cădariu and V. 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. 1