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Isometry on Linear n-G-quasi Normed Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Research Article
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- Copyright © Canadian Mathematical Society 2017