FUZZY STABILITY OF A FUNCTIONAL EQUATION RELATED TO INNER PRODUCT SPACES

Abstract

The fuzzy stability problems for the Cauchy quadratic functional equation and the Jensen quadratic functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Th. M. Rassias introduced the following equality Sigma(m)(i,j=1) parallel to xi - xj parallel to(2) = 2m Sigma(m)(i=1) parallel to x(i)parallel to(2), Sigma(m)(i=1) x(i) = 0, for a fixed integer m >= 3. By the above equality, we define the following functional equation (0.1) Sigma(m)(i,j=1) f(x(i) - x(j)) = 2m Sigma(m)(i=1) f(x(i)), Sigma(m)(i=1) x(i) = 0 In this paper, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.