Fixed points and fuzzy stability of an additive-quadratic functional equation

Ministry of Education, Science and TechnologyThe fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation lf (Sigma(l)(i=1)x(i)) + Sigma(l)(i=1)f(lx(i) - Sigma(l)(i=1)d(j)) (0.1) = l(2) + l/2 Sigma(l)(i=1)f(x(i)) + l(2) - l/2 Sigma(l)(i=1)f(-x(i)) (l >= 2) in fuzzy Banach spaces.Basic Science Research Program through the National Research Foundation of Kore

A FIXED POINT APPROACH TO THE STABILITY OF GENERAL QUADRATIC EULER-LAGRANGE FUNCTIONAL EQUATIONS IN INTUITIONISTIC FUZZY SPACES

In this paper, we prove the generalized Hyers-Ulam stability of a general k-quadratic Euler-Lagrange functional equation:for any fixed positive integer in intuitionistic fuzzy normed spaces using a fixed point method

On the Stability Problem in Fuzzy Banach Space

We investigate the generalized Ulam-Hyers stability of the Cauchy functional equation and pose two open problems in fuzzy Banach space

Hyers Stability in Generalized Intuitionistic P-Pseudo Fuzzy 2-Normed Spaces

In this article, we defined the generalized intuitionistic P-pseudo fuzzy 2-normed spaces and investigated the Hyers stability of m-mappings in this space. The m-mappings are interesting functional equations; these functional equations are additive for m = 1, quadratic for m = 2, cubic for m = 3, and quartic for m = 4. We have investigated the stability of four types of functional equations in generalized intuitionistic P-pseudo fuzzy 2-normed spaces by the fixed point method.This work is supported by the Basque Government under Grants IT1555-22 and KK-2022/00090 and MCIN/AEI 269.10.13039/501100011033 under Grant PID2021-1235430B-C21/C22

The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product Spaces

Th. M. Rassias (1984) proved that the norm defined over a real vector space is induced by an inner product if and only if for a fixed integer ≥2,∑=1‖∑−(1/)=1‖2=∑=1‖‖2∑−‖(1/)=1‖2 holds for all 1,…,∈. The aim of this paper is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation ∑=1(∑−(1/)=1∑)==1(∑)−((1/)=1) which is said to be a functional equation associated with inner product spaces