Abstract
In this paper we establish Hyers-Ulam-Rassias stability of a generalized functional equation in fuzzy Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-30.
Highlights
= (m − 1)2 2 m f (xi) i=1 where m is a positive integer greater than 3, in fuzzy Banach spaces
Katsaras [13] defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space
Cheng and Mordeson [2], gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Karmosil and Michalek type [14]
Summary
(Saadati and Vaezpour [31]) Let (X, N ) be a fuzzy normed vector space. It is well known that every convergent sequence in a fuzzy normed vector space is Cauchy. We say that a mapping f : X → Y between fuzzy normed vector spaces X and Y is continuous at a point x ∈ X if for each sequence {xn} converging to x0 ∈ X, the sequence {f (xn)} converges to f (x0).
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