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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 \[ \mu\circ f \circ\eta=f \] where \(\eta:X\to X, \mu:Y\to Y\) 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 \(F\).

39B52 Functional equations for functions with more general domains and/or ranges
39B82 Stability, separation, extension, and related topics for functional equations
47H10 Fixed-point theorems
54E70 Probabilistic metric spaces
Full Text: DOI
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