Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces

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.

Ulam Type Stability of ?-Quadratic Mappings in Fuzzy Modular ∗-Algebras

“…As noted in Example 1, (A, µ, • M )is a µ-complete convex fuzzy modular * -algebra and (R, µ .• M ) is a fuzzy modular space. The result follows from the fact that (4) and (5) are equivalent to(7) and(8), respectively.…”

“…for all x ∈ X. A number of mathematicians were attracted to this result and stimulated to investigate the stability problems of various(functional, differential, difference, integral) equations in some spaces [4][5][6][7][8][9][10][11].…”

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

“…The Ulam-Hyers stability (UHS) of fixed point problems and the fixed points of mappings over a locally convex topological vector space were presented by Roy et al [20]. Saha et al [21] provided a solution using FPT to the stability problems in intuitionistic fuzzy BSs. Alanazi et al [22] examined the fuzzy stability of a finite variable additive FE using direct and fixed point approaches.…”

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

“…In the year 2020, Saha et al [28] applied fixed point techniques to stability problems in intuitionistic fuzzy Banach spaces. In the same year, Alanazi et al [29] proved the fuzzy stability results of a finite variable additive functional equation using direct and fixed point methods.…”