Fuzzy Stability of Quadratic Functional Equations

Abstract

The 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. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations f (x + y ) + f (x - y) = 2f (x) + 2f (y) and f (ax + by) + f (ax - by) = 2a(2) f (x) + 2b(2) f (y) (a, b is an element of R\[0], a not equal +/- 1) in fuzzy Banach spaces.