The generalized hyers-ulam stability of sextic functional equation in various matrix spaces

Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following
generalized sextic functional equation 

Df (x, y):= f (mx+ y) +f (mx− y) +f(x+ my) +f(x− my)
− (m⁴+ m²) [f(x+ y+f(x− y)] −2(m⁶− m⁴− m²+ 1) [f(x) + f(y)]

in matrix fuzzy normed spaces. Furthermore, using the fixed point method, we also prove the
Hyers-Ulam stability of the above functional equation in matrix random normed spaces.

Keywords: Hyers-Ulam stability; fixed point method; matrix fuzzy normed space; matrix
random normed spaces; sextic functional equation.