Characterizations on isometries in linear \(n\)-normed spaces

DOI10.1016/j.na.2009.09.029zbMath1196.46011OpenAlexW2006723463MaRDI QIDQ2654012

Meimei Song, Xiao-yun Chen

Publication date: 15 January 2010

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.2009.09.029

zbMATH Keywords

\(n\)-isometrylinear \(n\)-normed spaceweak \(n\)-isometry

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) (46A70)

Related Items (16)

The Aleksandrov-Benz-Rassias problem on linear \(n\)-normed spaces ⋮ On the Hyers–Ulam stability and hyperstability of a generalized quadratic functional equation in n-Banach spaces ⋮ An introduction to 2-fuzzy \(n\)-normed linear spaces and a new perspective to the Mazur-Ulam problem ⋮ On \(n\)-norm preservers and the Aleksandrov conservative \(n\)-distance problem ⋮ Mazur-Ulam theorem under weaker conditions in the framework of 2-fuzzy 2-normed linear spaces ⋮ Approximation of two general functional equations in 2-Banach spaces ⋮ Stability of a general functional equation in \(m\)-Banach spaces ⋮ On the Hyers-Ulam stability of a general mixed additive and cubic functional equation in \(n\)-Banach spaces ⋮ The Aleksandrov problem on non-Archimedean normed space ⋮ On Ulam stability of a functional equation ⋮ On the Mazur-Ulam theorem in non-Archimedean fuzzy \(n\)-normed spaces ⋮ Two equivalent \(n\)-norms on the space of \(p\)-summable sequences ⋮ A Tingley's type problem in \(n\)-normed spaces ⋮ A fixed point theorem in \(n\)-Banach spaces and Ulam stability ⋮ Mappings preserving unit distance on Heisenberg group ⋮ Approximate multi-Jensen, multi-Euler-Lagrange additive and quadratic mappings in \(n\)-Banach spaces

Cites Work

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• On the Mazur--Ulam problem in linear 2-normed spaces
• The Aleksandrov problem in linear 2-normed spaces.
• On the Aleksandrov problem in linear \(n\)-normed spaces
• On the A.D. Aleksandrov problem of conservative distances and the Mazur-Ulam theorem.
• Characterizations on 2-isometries
• Orthogonality and Orthonormality inn-Inner Product Spaces
• n-Inner Product Spaces
• On the Aleksandrov Problem of Conservative Distances
• On the Mazur-Ulam Theorem and the Aleksandrov Problem for Unit Distance Preserving Mappings

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