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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 $\left(Y,F,{T}_{M}\right)$ with ${T}_{M}\left(a,b\right)=min\left(a,b\right)$ and probabilistic distance $F$.

##### MSC:
 39B52 Functional equations for functions with more general domains and/or ranges 39B82 Stability, separation, extension, and related topics 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 54E70 Probabilistic metric spaces
##### References:
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