On the stability of an m-variables functional equation in random normed spaces via fixed point method

Abstract

At first we find the solution of the functional equation Df (x1,⋯, xm) := ∑k=2m (∑i1=2k ∑i2=i1+1k+1 ⋯ ∑im-k+1=im-k+1m) f (∑ i=1,i≠i1,⋯im-k+1m xi - ∑r=1m-k+1 xir)+f (∑i=1m xi) 2m-1 f (x1) = 0, where m ≥ 2 is an integer number. Then, we obtain the generalized Hyers-Ulam-Rassias stability in random normed spaces via the fixed point method for the above functional equation. Copyright © 2012 A. Ebadian et al.