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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 $$F$$.

##### MSC:
 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
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