The Aleksandrov Problem and the mazur-ulam theorem for unit Distance Preserving Mappings on Linear n-normed Spaces

Ma Yumei

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The Aleksandrov Problem and the mazur-ulam theorem for unit Distance Preserving Mappings on Linear n-normed Spaces

机译：线性n范空间上单位距离保留映射的Aleksandrov问题和mazur-ulam定理

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摘要

In this paper, we show that if f satisfies nDOPP, then the following five concepts are equivalent: w-n-isometry,w-n-Lipschitz,2-colinear.

机译：在本文中，我们表明，如果f满足nDOPP，则以下五个概念是等效的：w-n-等距，w-n-Lipschitz，2-共线性。

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来源
《Pacific journal of applied mathematics》 |2012年第3期|共11页
作者
Ma Yumei;
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正文语种 eng
中图分类 O2;
关键词
Aleksandrov problems; Mazur-Ulam; linear n-normed space; w-n-isometry; w-n-Lipschitz mapping; w-n-DOPP; 2-colinear;

机译：Aleksandrov问题;Mazur-Ulam;线性n范空间;w-n-等距;w-n-Lipschitz映射;w-n-DOPP;2-共线性;

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1. The Aleksandrov Problem and the mazur-ulam theorem for unit Distance Preserving Mappings on Linear n-normed Spaces [J] . Ma Yumei Pacific journal of applied mathematics . 2012,第3期

机译：线性n范空间上单位距离保留映射的Aleksandrov问题和mazur-ulam定理
2. A new version of Mazur-Ulam theorem under weaker conditions in linear n-normed spaces [J] . Choonkil Park, Cihangir Alaca Journal of computational analysis and applications . 2014,第5期

机译：线性n赋范空间中弱条件下的Mazur-Ulam定理的新版本
3. The Aleksandrov problem and the Mazur-Ulam theorem on linear $n$-normed spaces [J] . Ma Yumei Bulletin of the Korean Mathematical Society . 2013,第5期

机译：线性$ n $赋范空间上的Aleksandrov问题和Mazur-Ulam定理
4. A Mazur-Ulam theorem for normed gyrolinear spaces [C] . Toshikazu Abe Workshop on Problems and Recent Methods in Operator Theory . 2017

机译：适用于规范的陀螺空间的Mazur-Ulam定理
5. Invariant manifolds, invariant foliations and linearization theorems in Banach spaces. [D] . Tan, Bin. 1998

机译：Banach空间中的不变流形，不变叶面和线性化定理。
6. MAPPING THEOREMS FOR NONCOMPACT NONLINEAR OPERATORS IN BANACH SPACES [O] . Felix E. Browder 1965

机译：Banach空间中非紧非线性算子的映射定理。
7. A Mazur-Ulam theorem for Mappings of conservative distance in non-Archimedean $n$-normed spaces [O] . Chu, Hahng-Yun, Ku, Se-Hyun 2009

机译：mazur-Ulam定理的保守距离映射非阿基米德$ n $ -normed空格

The Aleksandrov Problem and the mazur-ulam theorem for unit Distance Preserving Mappings on Linear n-normed Spaces

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