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ON THE ALEKSANDROV–RASSIAS PROBLEM OF DISTANCE PRESERVING MAPPINGS

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  17 March 2015

SHUMING WANG  and
WEIYUN REN
SHUMING WANG*
Affiliation:
School of Science, Tianjin University, Tianjin 300072, China email wsmmath@163.com
WEIYUN REN
Affiliation:
School of Science, Tianjin University, Tianjin 300072, China email rwyun@163.com
*
✉wsmmath@163.com
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Abstract

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In this paper, we introduce the concept of a semi-parallelogram and obtain some results for the Aleksandrov–Rassias problem using this concept. In particular, we resolve an important case of this problem for mappings preserving two distances with a nonintegral ratio.

Keywords

isometryAleksandrov problemconservative distancesemi-parallelograminner product space

MSC classification

Primary: 46B04: Isometric theory of Banach spaces
Secondary: 46B20: Geometry and structure of normed linear spaces 46C05: Hilbert and pre-Hilbert spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 3 , June 2015 , pp. 464 - 470
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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