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

摘要

At first we find the solution of the functional equation ??(?1,…,??)∶=∑??=2(∑??1=2∑?+1?2=?1+1⋯∑???−?+1=??−?+1)?(∑??=1,?≠?1,…,??−?+1??−∑?−?+1?=1???)+?(∑??=1??)−2?−1?(?1)=0, where ?≥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.