Abstract
The object of this article is to determine Hyers-Ulam-Rassias stability results concerning the cubic functional equation in fuzzy normed space by using the fixed point method.
Highlights
1 Introduction, definitions and notations Fuzzy set theory is a powerful hand set for modeling uncertainty and vagueness in various problems arising in the field of science and engineering
By modifying own studies on fuzzy topological vector spaces, Katsaras [12] first introduced the notion of fuzzy seminorm and norm on a vector space and later on Felbin [13] gave the concept of a fuzzy normed space by applying the notion fuzzy distance of Kaleva and Seikala [14] on vector spaces
Stability problem of a functional equation was first posed by Ulam [16] which was answered by Hyers [17] under the assumption that the groups are Banach spaces
Summary
Introduction, definitions and notations Fuzzy set theory is a powerful hand set for modeling uncertainty and vagueness in various problems arising in the field of science and engineering. Xiao and Zhu [15] improved a bit the Felbin’s definition of fuzzy norm of a linear operator between FNSs. Stability problem of a functional equation was first posed by Ulam [16] which was answered by Hyers [17] under the assumption that the groups are Banach spaces. The unified form of the results of Hyers, Rassias, and Gajda is as follows: Let E and F be real normed spaces with F complete and let f : E ® F be a mapping such that the following condition holds f x + y − f (x) − f y F ≤ θ x p E
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