The Aleksandrov-Rassias problem on quasi convex n-normed linear spaces

Abstract

We proved that the Aleksandrov-Rassias problem holds repalced the condition $ \parallel x_{1}-y_{1},\ldots, x_{n}-y_{n} \parallel \geq1$ if and only if $\parallel f(x_{1})-f(y_{1}), f(x_{2})-f(y_{2}), \cdots, f(x_{n})-f(y_{n})\parallel \geq1 $ " in [7] by ``$\parallel f(x_{1})-f(y_{1}), f(x_{2})-f(y_{2}), \cdots, f(x_{n})-f(y_{n})\parallel \leq \parallel x_{1}-y_{1},\ldots, x_{n}-y_{n} \parallel $ while $ \parallel x_{1}-y_{1},\ldots, x_{n}-y_{n} \parallel\leq1$" on Quasi Convex n-normed linear Spaces.