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Zbl 1187.39044
Miheţ, Dorel
The probabilistic stability for a functional nonlinear equation in a single variable.
(English)
[J] J. Math. Inequal. 3, No. 3, 475-483 (2009). ISSN 1846-579X

After an introduction where the notions of generalized metric space and probabilistic metric space are presented and where some fixed point theorems in those settings are given, the author proves the probabilistic Hyers-Ulam stability for the functional equation $$f(x)=\Phi(x,f(\eta(x))),$$ where the unknown is a mapping $f$ from a non empty set $S$ to a complete probabilistic metric space $(X,F,T_M)$ and $\Phi:S \times X \to X$, $\eta:S \to X$ are given functions.
[Gian Luigi Forti (Milano)]
MSC 2000:
*39B82 Stability, separation, extension, and related topics
39B52 Functional equations for functions with more general domains
54E70 Probabilistic metric spaces

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

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