Fuzzy normed spaces and stability of a generalized quadratic functional equation

Abstract

In this paper, we acquire the general solution of the generalized quadratic functional equation

Sigma(1 ˂= a ˂= b ˂= c ˂= m) phi(r(a) + r(b) + r(c)) = (m - 2) Sigma(1 ˂= a ˂= b ˂= m) phi(r(a) + r(b))

-(m(2) - 3m + 2/2) Sigma(m)(a=1) phi(r(a)) + phi(-r(a))/2

where in m ˃= 3 is an integer. We also investigate Hyers-Ulam stability results by means of using alternative fixed point theorem for this generalized quadratic functional equation.