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The probabilistic stability for a functional equation in a single variable. (English) Zbl 1212.39036

By using the fixed point method, the author deals with the probabilistic Hyers-Ulam stability and the generalized Hyers-Ulam-Rassias stability of the functional equation

μfη=f

where η:XX,μ:YY are given functions and f is the unknown mapping from X to a probabilistic metric space (Y,F,T M ) with T M (a,b)=min(a,b) and probabilistic distance F.

MSC:
39B52Functional equations for functions with more general domains and/or ranges
39B82Stability, separation, extension, and related topics
47H10Fixed point theorems for nonlinear operators on topological linear spaces
54E70Probabilistic metric spaces
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