Approximate solution of a multivariable Cauchy-Jensen functional equation

Abstract

Let $ n $ be an integer greater than $ 1 $. In this paper, we obtained the stability of the multivariable Cauchy-Jensen functional equation $ nf\bigg(x_1+{\cdots}+x_n, \frac {y_1+{\cdots}+y_n}n\bigg) = \sum\limits_{1\le i, j\le n}f(x_i, y_j) $ in Banach spaces, quasi-Banach spaces, and normed $ 2 $-Banach spaces.

Keywords

• linear $ 2 $-normed space
• quasi-normed space
• cauchy-jensen mapping