Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 973-981

ISOMETRY ON LINEAR n-NORMED SPACES

Yumei Ma

Dalian Nationalities University, Department of Mathematics
116600 Dalian, P.R. China; mayumei1962 'at' 163.com

Abstract. This paper generalizes the Aleksandrov problem, the Mazur-Ulam theorem and Benz theorem on n-normed spaces. It proves that a one-distance preserving mapping is an n-isometry if and only if it has the zero-distance preserving property, and two kinds of n-isometries on n-normed spaces are equivalent.

2010 Mathematics Subject Classification: Primary 46B04, 46B20, 51K05.

Key words: Mazur-Ulam theorem, Aleksandrov problem, n-isometry, n-Lipschitz, n-0-distance.

Reference to this article: Y. Ma: Isometry on linear n-normed spaces. Ann. Acad. Sci. Fenn. Math. 39 (2014), 973-981.

Full document as PDF file

doi:10.5186/aasfm.2014.3941