Geodesic
Isometry on Linear n-G-quasi Normed Spaces
Canadian mathematical bulletin, Tome 60 (2017) no. 2, pp. 350-363

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DOI

This paper generalizes the Aleksandrov problem: the Mazur-Ulam theorem on $n-G$ -quasi normed spaces. It proves that a one- $n$ -distance preserving mapping is an $n$ -isometry if and only if it has the zero- $n-G$ -quasi preserving property, and two kinds of $n$ -isometries on $n-G$ -quasi normed space are equivalent; we generalize the Benz theorem to $n$ -normed spaces with no restrictions on the dimension of spaces.
DOI : 10.4153/CMB-2016-061-9
Mots-clés : 46B20, 46B04, 51K05, n-G-quasi norm, Mazur–Ulam theorem, Aleksandrov problem, n-isometry, n-0-distance 
Ma, Yumei. Isometry on Linear n-G-quasi Normed Spaces. Canadian mathematical bulletin, Tome 60 (2017) no. 2, pp. 350-363. doi: 10.4153/CMB-2016-061-9
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     author = {Ma, Yumei},
     title = {Isometry on {Linear} {n-G-quasi} {Normed} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {350--363},
     year = {2017},
     volume = {60},
     number = {2},
     doi = {10.4153/CMB-2016-061-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-061-9/}
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