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December 2015 Mappings preserving unit distance on Heisenberg group
J.M. Rassias, A. Charifi, Ab. Chahbi, S. Kabbaj
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Tbilisi Math. J. 8(2): 131-137 (December 2015). DOI: 10.1515/tmj-2015-0016

Abstract

Let $H^{m}$ be a Heisenberg group provided with a norm $\rho$. A mapping $f:H^{m}\rightarrow H^{m}$ is called preserving the distance $n$ if for all $x,y$ of $H^{m}$ with $\rho(x^{-1}y)=n$ then $\rho(f(x)^{-1}f(y))=n$. We obtain some results for the Aleksandrov problem in the Heisenberg group.

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J.M. Rassias. A. Charifi. Ab. Chahbi. S. Kabbaj. "Mappings preserving unit distance on Heisenberg group." Tbilisi Math. J. 8 (2) 131 - 137, December 2015. https://doi.org/10.1515/tmj-2015-0016

Information

Received: 4 December 2014; Accepted: 15 June 2015; Published: December 2015
First available in Project Euclid: 12 June 2018

zbMATH: 1321.39035
MathSciNet: MR3383788
Digital Object Identifier: 10.1515/tmj-2015-0016

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

Rights: Copyright © 2015 Tbilisi Centre for Mathematical Sciences

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Vol.8 • No. 2 • December 2015
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