Title : Mirmostafaee, Alireza Kamel; Moslehian, Mohammad Sal\\ ( Fuzzy stability of the Jensen functional equation )
Authors: Seyyed Alireza Kamel Mirmostafaee , Madjid Mirzavaziri , Mohammad Sal Moslehian ,
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Abstract
We establish a generalized Hyers–Ulam–Rassias stability theorem in the fuzzy sense. In particular, we introduce the notion of fuzzy approximate Jensen mapping and prove that if a fuzzy approximate Jensen mapping is continuous at a point, then we can approximate it by an everywhere continuous Jensen mapping. As a fuzzy version of a theorem of Schwaiger, we also show that if every fuzzy approximate Jensen type mapping from the natural numbers into a fuzzy normed space can be approximated by an additive mapping, then the fuzzy norm is complete.
Keywords
Fuzzy normed space; Jensen functional equation; Additive mapping; Hyers–Ulam–Rassias stability; Continuity; approximately additive
@article{paperid:1004940,
author = {Kamel Mirmostafaee, Seyyed Alireza and Madjid Mirzavaziri, and Sal Moslehian, Mohammad},
title = {Mirmostafaee, Alireza Kamel; Moslehian, Mohammad Sal\\},
journal = {Fuzzy Sets and Systems},
year = {2008},
volume = {159},
number = {6},
month = {November},
issn = {0165-0114},
pages = {730--738},
numpages = {8},
keywords = {Fuzzy normed space; Jensen functional equation; Additive mapping; Hyers–Ulam–Rassias stability; Continuity; approximately additive},
}
%0 Journal Article
%T Mirmostafaee, Alireza Kamel; Moslehian, Mohammad Sal\\
%A Kamel Mirmostafaee, Seyyed Alireza
%A Madjid Mirzavaziri,
%A Sal Moslehian, Mohammad
%J Fuzzy Sets and Systems
%@ 0165-0114
%D 2008
