Fuzzy stability of the Jensen functional equation

Authors:
A. K. Mirmostafaee;M. Mirzavaziri;M. S. Moslehian
Affiliations:
Department of Mathematics, Damghan University of Basic Sciences, Damghan, Iran and Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran and Centre of Excellence in An ...;Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran and Banach Mathematical Research Group (BMRG), Mashhad, Iran;Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran and Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University, Iran
Venue:
Fuzzy Sets and Systems
Year:
2008

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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.