The Orlicz Aleksandrov Problem for Orlicz Integral Curvature

In this paper, the Orlicz integral curvature is introduced, and some of its basic properties are discussed. The Orlicz Aleksandrov problem characterizing the Orlicz integral curvature is posed. The problem is solved in two situations when the given measure is even.

Isometry on Linear n-G-quasi Normed Spaces

This 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.