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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… Click to show full abstract
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.
Keywords:
linear quasi;
isometry linear;
quasi normed;
normed spaces
Journal Title: Canadian Mathematical Bulletin
Year Published: 2017
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Journal Title: Canadian Mathematical Bulletin
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!