On the Aleksandrov problem in linear \(n\)-normed spaces

DOI10.1016/J.NA.2004.07.046zbMath1066.46005OpenAlexW1996615066MaRDI QIDQ1765201

Hahng-Yun Chu, Chun-Gil Park, Keon-Hee Lee

Publication date: 23 February 2005

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.07.046

zbMATH Keywords

\(n\)-isometry\(n\)-Lipschitz mappinglinear \(n\)-normed space

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) (46A70) General theory of distance geometry (51K05) Isometric theory of Banach spaces (46B04)

Related Items (14)

The Aleksandrov-Benz-Rassias problem on linear \(n\)-normed spaces ⋮ Mappings of preserving \(n\)-distance one in \(n\)-normed spaces ⋮ On the Mazur--Ulam problem in linear 2-normed spaces ⋮ Characterizations on isometries in linear \(n\)-normed spaces ⋮ On the Aleksandrov-Rassias problems on linear \(n\)-normed spaces ⋮ On \(n\)-norm preservers and the Aleksandrov conservative \(n\)-distance problem ⋮ The \(N\)-isometric isomorphisms in linear \(N\)-normed \(C^{\ast}\)-algebras ⋮ The Aleksandrov problem on non-Archimedean normed space ⋮ GENERALIZATIONS OF ALESANDROV PROBLEM AND MAZUR-ULAM THEOREM FOR TWO-ISOMETRIES AND TWO-EXPANSIVE MAPPINGS ⋮ On the Mazur-Ulam theorem in non-Archimedean fuzzy \(n\)-normed spaces ⋮ Inequalities in additive \(N\)-isometries on linear \(N\)-normed Banach spaces ⋮ A Tingley's type problem in \(n\)-normed spaces ⋮ A fixed point theorem in \(n\)-Banach spaces and Ulam stability ⋮ Mappings of conservative distances in linear \(n\)-normed spaces

Cites Work

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• Properties of isometric mappings
• The Aleksandrov problem in linear 2-normed spaces.
• On the A.D. Aleksandrov problem of conservative distances and the Mazur-Ulam theorem.
• On the Aleksandrov Problem of Conservative Distances
• On the Mazur-Ulam Theorem and the Aleksandrov Problem for Unit Distance Preserving Mappings
• Mappings of conservative distances and the Mazur-Ulam theorem

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