The probabilistic stability for a functional equation in a single variable
type: Item
instance of: scholarly article
title: The probabilistic stability for a functional equation in a single variable
zbMATH Open document ID: 1212.39036
author: Dorel Miheţ
published in: Acta Mathematica Hungarica
publication date: 2009-12-29T00:00:00Z
review text: 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 \(F\).
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54E70
zbMATH DE Number: 5652019
zbMATH Keywords: functional equation
zbMATH Keywords: fixed points method
zbMATH Keywords: probabilistic metric space
zbMATH Keywords: probabilistic Hyers-Ulam stability
zbMATH Keywords: generalized Hyers-Ulam-Rassias stability
MaRDI profile type: Publication
full work available at URL: s10474-008-8101-y
OpenAlex ID: W2137323058
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DOI: 10.1007/S10474-008-8101-Y
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description: scientific article; zbMATH DE number 5652019