On the Stability of anm-Variables Functional Equation in Random Normed Spaces via Fixed Point Method

摘要

At first we find the solution of the functional equationDf(x1,…,xm):=∑k=2m(∑i1=2k∑i2=i1+1k+1⋯∑im-k+1=im-k+1m)f(∑i=1,i≠i1,…,im-k+1mxi-∑r=1m-k+1xir)+f(∑i=1mxi)-2m-1f(x1)=0,wherem≥2is 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.