Stability of quadratic functional equations in random normed spaces

Abstract

In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations cf(∑ni=1xi)+∑nj=2f(∑ni=1xi-(n + c - 1)xj)=(n + c - 1)(f(x1) + c∑ni=2f(xi) + ∑ni<j,j=3(∑n-1i=2f(xi - xj))),Q(∑ni=1dixi)+∑1≤i<j≤n didjQ(xi - xj) = (∑ni=1 di)(∑ni=1 diQ(xi))in random normed spaces.