Nearly Radical Quadratic Functional Equations in p-2-Normed Spaces

Abstract

We establish some stability results in 2-normed spaces for the radical quadratic functional equation $f\left(\sqrt{{\sum }_{i=1}^n(x_i+y_i{)}^2}\right)+f\left(\sqrt{{\sum }_{i=1}^n(x_i-y_i{)}^2}\right)=2{\sum }_{i=1}^n\left(f\left(x_i\right)+f\left(y_i\right)\right)$ and then use subadditive functions to prove its stability in $p$-2-normed spaces.