Fuzzy stability of an additive-quadratic functional equation in matrix fuzzy normed spaces

Abstract

A mapping f: X x X -> Y is called additive-quadratic if f satisfies the system of equations

{ f(x + y, z) = f(x, z) + f (y, z), f(x, y + z) + f(x, y-z) = 2f(x,y) + 2f(x,z).

In this paper, using the fixed point method, we prove the Hyers-Ulam stability in matrix fuzzy normed spaces associated to the following additive-quadratic functional equation

f (x + y, z + w) + f (x + y, z - w) = 2f (x, z) + 2f (x, w) + 2f(y,z) + 2f (y, w)

for all x,y, z,w is an element of X.