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

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.