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2007 On the Aleksandrov-Rassias problem and the Hyers-Ulam-Rassias stability problem
Liyun Tan, Shuhuang Xiang
Banach J. Math. Anal. 1(1): 11-22 (2007). DOI: 10.15352/bjma/1240321551

Abstract

Let $X$ and $Y$ be normed linear spaces. A mapping $T:X \rightarrow Y$ is called preserving the distance $r$ if for all $x,y$ of $X$ with $\|x-y\|_X=r$ then $\|T(x)-T(y)\|=r$. In this paper, we provide an overall account of the development of the Aleksandrov problem, the Aleksandrov-Rassias problem for mappings which preserve distances and details for the Hyers-Ulam-Rassias stability problem.

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Liyun Tan. Shuhuang Xiang. "On the Aleksandrov-Rassias problem and the Hyers-Ulam-Rassias stability problem." Banach J. Math. Anal. 1 (1) 11 - 22, 2007. https://doi.org/10.15352/bjma/1240321551

Information

Published: 2007
First available in Project Euclid: 21 April 2009

zbMATH: 1130.39027
MathSciNet: MR2350190
Digital Object Identifier: 10.15352/bjma/1240321551

Subjects:
Primary: 39B82
Secondary: 44B20‎ , 46C05

Keywords: additive mapping , conservative distance , isometry , stability

Rights: Copyright © 2007 Tusi Mathematical Research Group

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