Stability of an n -Dimensional Mixed-Type Additive and Quadratic Functional Equation in Random Normed Spaces

Abstract

We investigate the stability problems for the $n$-dimensional mixed-type additive and quadratic functional equation $2f\left({\sum }_{j=1}^n{x}_j\right)+{\sum }_{1\le i,j\le n,i\ne j}f(x_i-x_j)=(n+1){\sum }_{j=1}^{n}f\left(x_j\right)+(n-1){\sum }_{j=1}^{n}f(-x_j)$ in random normed spaces by applying the fixed point method.