Solution and intuitionistic fuzzy stability of n- dimensional quadratic functional equation: direct and fixed point methods

Abstract

In this paper, the authors established the solution in vector space and Intuitionistic Fuzzy stability of n-dimensional quadratic functional equation

Stability of a Functional equation originating from sum of first l natural numbers in Intuitionistic Fuzzy Banach Space and Algebras using Direct and Fixed Point Methods

“…for all w ∈ N 1 and all η > 0. Letting α → ∞ in ( 35), ( 36) and using (15), one can notice that Ψ(w) satisfies the functional equation (12). In order to prove the existence of Ψ(w) is unique, let Φ(w) be another additive functional equation satisfying (12) and (18).…”

“…Lee [25], K. Ravi, M. Arunkumar [46], M. Arunkumar [3,4,5,6,7,10], J. M. Rassias et.al., [43]. The generalized Ulam -Hyers stability of several functional equations in various Banach spaces including Intuitionistic Fuzzy Banach spaces and Algebras were investigated in [8,9,11,12,15,16,17,18,19,21,13,14,43].…”

Stability Results of Additive-Quadratic \(n\)-Dimensional Functional Equation

“…In 2008, a special case of Gavruta's theorem for the unbounded Cauchy difference was obtained by Ravi et al [27] by considering the summation of both the sum and the product of two p-norms in the spirit of Rassias approach. The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [2,4,5,17,18,22,27]) and reference cited there in.…”

Ulam-Hyers stability of quadratic reciprocal functional equation in intuitionistic random normed spaces: Various methods

“…In 2014, M. Arunkumar and S. Karthikeyan [5] introduced and investigated Hyers-Ulam stability of ndimensional reciprocal functional equation…”