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

Fuzzy approximately additive mappings

Abstract. Moslehian and Mirmostafaee, investigated the fuzzy stability problems for the Cauchy additive functional equation, the Jensen additive functional equation and the cubic functional equation in fuzzy Banach spaces. In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of the generalized additive functional equation with n-variables, in fuzzy Banach spaces. Also, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost additive function, control function and the unique additive function which approximate the almost additive function

Intuitionistic fuzzy stability of a quadratic and quartic functional equation

Abstract. In this paper, we prove the generalized Hyers-Ulam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces