Isometry on Linear n-G-quasi Normed Spaces

Abstract

AbstractThis paper generalizes the Aleksandrov problem: the Mazur-Ulam theoremon n-G-quasi normed spaces. It proves that a one-n-distance preserving mapping is an n-isometry if and only if it has the zero-n-G-quasi preserving property, and two kinds of n-isometries on n-G-quasi normed space are equivalent; we generalize the Benz theorem to n-normed spaces with no restrictions on the dimension of spaces.