Stability of the n -Dimensional Mixed-Type Additive and Quadratic Functional Equation in Non-Archimedean Normed Spaces

Abstract

We will prove the stability of the functional equation $2f\left({\sum }_{i=1}^n{x}_i\right)+$ ${\sum }_{1\le i,j\le n,i\ne j}f(x_i-x_j)=$ $(n+1){\sum }_{i=1}^{n}f\left(x_i\right)+(n-1){\sum }_{i=1}^{n}f(-x_i)$ in non-Archimedean normed spaces.