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

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. 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.