On the Aleksandrov-Rassias problems on linear \(n\)-normed spaces
type: Item
instance of: scholarly article
title: On the Aleksandrov-Rassias problems on linear \(n\)-normed spaces
zbMATH Open document ID: 1283.46010
DOI: 10.1155/2013/394216
author: Yumei Ma
published in: Journal of Function Spaces and Applications
publication date: 2013-08-30T00:00:00Z
review text: Summary: This paper generalizes results of \textit{Th. M. Rassias} and \textit{P. Šemrl} [Proc. Am. Math. Soc. 118, No. 3, 919--925 (1993; Zbl 0780.51010)] to \(n\)-normed spaces. If \(X\) and \(Y\) are two real \(n\)-normed spaces and \(Y\) is \(n\)-strictly convex, a surjective mapping \(f : X \to Y\) preserving the unit distance in both directions and preserving any integer distance is an \(n\)-isometry.
Mathematics Subject Classification ID: 46B04
zbMATH DE Number: 6203149
zbMATH Keywords: \(n\)-normed space
zbMATH Keywords: \(n\)-isometry
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/394216
OpenAlex ID: W2051841373
Wikidata QID: Q59014072
cites work: Q5615895
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description: scientific article; zbMATH DE number 6203149