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Convexity without convex combinations

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Abstract

Separation theorems play a central role in the theory of Functional Inequalities. The importance of Convex Geometry has led to the study of convexity structures induced by Beckenbach families. The aim of the present note is to replace recent investigations into the context of an axiomatic setting, for which Beckenbach structures serve as models. Besides the alternative approach, some new results (whose classical correspondences are well-known in Convex Geometry) are also presented.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, Pf. 12, 4010, Debrecen, Hungary

    Mihály Bessenyei & Bella Popovics

Authors
  1. Mihály Bessenyei
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  2. Bella Popovics
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Correspondence to Mihály Bessenyei.

Additional information

This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grants K–111651 and by the SROP-4.2.2.B-15/1/KONV-2015-0001 project. The project has been supported by the European Union, co-financed by the European Social Fund.

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Bessenyei, M., Popovics, B. Convexity without convex combinations. J. Geom. 107, 77–88 (2016). https://doi.org/10.1007/s00022-015-0276-0

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  • DOI: https://doi.org/10.1007/s00022-015-0276-0

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