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Zbl 1212.39036
Miheţ, D.
The probabilistic stability for a functional equation in a single variable. (English)
[J] Acta Math. Hung. 123, No. 3, 249-256 (2009). ISSN 0236-5294; ISSN 1588-2632/e

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 $F$.
[Gyula Maksa (Debrecen)]

MSC 2000:: *39B52 Functional equations for functions with more general domains
39B82 Stability, separation, extension, and related topics
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54E70 Probabilistic metric spaces

Keywords: functional equation; fixed points method; probabilistic metric space; probabilistic Hyers-Ulam stability; generalized Hyers-Ulam-Rassias stability

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Zentralblatt MATH Berlin [Germany]