On orthogonal chords in normed planes

DOI10.1216/RMJ-2011-41-1-23zbMath1214.52001OpenAlexW2059518611MaRDI QIDQ627370

Horst Martini, Javier Alonso, Zokhrab Mustafaev

Publication date: 1 March 2011

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-2011-41-1-23

zbMATH Keywords

isosceles orthogonalityconstant widthmaximal chordBirkhoff orthogonalitynormed planeconvex figure

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (2) dimensions (including convex curves) (52A10) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items (5)

Orthogonality Types in Normed Linear Spaces ⋮ On the calculation of the Dunkl-Williams constant of normed linear spaces ⋮ On a question of Makai and Martini on bodies of~constant width ⋮ On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces ⋮ A new type of orthogonality for normed planes

Cites Work

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• On Reuleaux triangles in Minkowski planes
• A new characterization of convex plates of constant width
• Characterizations of inner product spaces
• Metrics compatible with a symmetric connection in dimension three
• The geometry of Minkowski spaces -- a survey. II.
• Orthogonality in linear metric spaces
• Some Characterizations of Inner-Product Spaces
• Orthogonality and Linear Functionals in Normed Linear Spaces
• Orthogonality in normed linear spaces

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