Abstract
In this paper we investigate Hyers-Ulam-Rassias stability of certain nonlinear functional equations. Considerations of such stabilities in different branches of mathematics have been very extensive. Again the fuzzy concepts along with their several extensions have appeared in almost all branches of mathematics. Here we work on intuitionistic fuzzy real Banach spaces, which is obtained by combining together the concepts of fuzzy Banach spaces with intuitionistic fuzzy sets. We establish that pexiderized quadratic functional equations defined on such spaces are stable in the sense of Hyers-Ulam-Rassias stability. We adopt a fixed point approach to the problem. Precisely, we use a generxalized contraction mapping principle. The result is illustrated with an example.
Highlights
In this paper, we derive Hyers-Ulam-Rassias stability results for certain functional equations in the context of intuitionistic fuzzy Banach spaces (IFBS)
H-U-R stability for functional equations on linear spaces has been discussed in quite a large number of papers, some of which are noted in [7,8,9,10,11,12,13,14]
Amongst several approaches to H-U-R stability problems we adopt the fixed point approach where the stability is established through an application of a fixed point theorem obtained in complete generalized metric spaces [25]
Summary
We derive Hyers-Ulam-Rassias stability results for certain functional equations in the context of intuitionistic fuzzy Banach spaces (IFBS). The problem of stability that we study here was for the first time mathematically formulated by Ulam [1] It was partly solved and further generalized by Hyers [2] and Rassias [3]. Today we know such stability problems as the problems of the Hyers-Ulam-Rassias (H-U-R) stability It has many extended forms and has been studied in several domains of mathematics including differential equations [4], functional equations [5], isometries [6], etc. In this paper we consider the H-U-R stability problem for pexiderized quadratic functional equations These equations are generalized quadratic functional equations and appeared in the literature in works like [22,23,24]. Amongst several approaches to H-U-R stability problems we adopt the fixed point approach where the stability is established through an application of a fixed point theorem obtained in complete generalized metric spaces [25]
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