3 Dimensional additive quadratic functional equation

Abstract

In this paper, the authors established the general solution and generalized Ulam - Hyers stability of an 3 dimensional additive quadratic functional equation$$\begin{aligned}& h(x+2 y+3 z)+h(x+2 y-3 z)+h(x-2 y+3 z)+h(-x+2 y+3 z) \\&=h(x+y+z)+h(x+y-z)+h(x-y+z)+h(-x+y+z) \\&+2 h(y)+4 h(z)+5[h(y)+h(-y)]+14[h(z)+h(-z)]\end{aligned}$$via Banach space and non-Archimedean fuzzy Banach Space using direct and fixed point methods.