Fuzzy Stability of the Generalized Version of Drygas Functional Equation

Abstract

We consider the functional equation $f(ax+y)+f(ax-y)-a(a+1)f(x)-a(a-1)f(-x)-[f(y)+f(-y)]$ $+k[f(x+y)+f(x-y)-2f(x)-f(y)-f(-y)]=0$ for a fixed rational number $a$ with $a\ne 1,-\mathrm{1,0}$ and a fixed real number $k$. We study the solution of the equation between linear spaces and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy normed space.