Mappings of conservative distances and the Mazur-Ulam theorem

DOI10.1006/jmaa.2000.7276zbMath0971.47001OpenAlexW2049281040MaRDI QIDQ5927727

Shuhuang Xiang

Publication date: 4 November 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.7276

zbMATH Keywords

Hilbert spaceAleksandrov-Rassias problemEuclidean spaceisometryparallelogram

Mathematics Subject Classification ID

General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Related Items (13)

An inequality for distances between \(2n\) points and the Aleksandrov--Rassias problem ⋮ An introduction to 2-fuzzy \(n\)-normed linear spaces and a new perspective to the Mazur-Ulam problem ⋮ The \(N\)-isometric isomorphisms in linear \(N\)-normed \(C^{\ast}\)-algebras ⋮ A Mazur-Ulam problem in non-Archimedean \(n\)-normed spaces ⋮ Mazur-Ulam theorem under weaker conditions in the framework of 2-fuzzy 2-normed linear spaces ⋮ An inequality for distances among five points and distance preserving mappings ⋮ The Aleksandrov problem in linear 2-normed spaces. ⋮ Inequalities in additive \(N\)-isometries on linear \(N\)-normed Banach spaces ⋮ Inequalities for distances between points and distance preserving mappings ⋮ On the Aleksandrov problem in linear \(n\)-normed spaces ⋮ The distance preserving mappings and isometrics defined on non-Archimedean Banach spaces ⋮ Mappings of conservative distances in linear \(n\)-normed spaces ⋮ ON THE ALEKSANDROV–RASSIAS PROBLEM OF DISTANCE PRESERVING MAPPINGS

Cites Work

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• A contribution to a theorem of Ulam and Mazur
• Properties of isometric mappings
• Hyperbolic distances in Hilbert spaces
• Is a Distance One Preserving Mapping between Metric Spaces Always an Isometry?
• On the Aleksandrov Problem of Conservative Distances
• On the Mazur-Ulam Theorem and the Aleksandrov Problem for Unit Distance Preserving Mappings
• On the asymptoticity aspect of Hyers-Ulam stability of mappings
• Isometries in Normed Spaces
• On Isometries of Euclidean Spaces
• Isometries and approximate isometries

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