Journal Article10.1007/S00022-015-0276-0
Convexity without convex combinations
Mihály Bessenyei,Bella Popovics +1 more
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TL;DR: In this paper, the authors replace recent investigations into the context of an axiomatic setting, for which Beckenbach structures serve as models, by an alternative approach, and some new results (whose classical correspondences are well-known in Convex Geometry) are also presented.
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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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•Posted Content
A sandwich with segment convexity
TL;DR: In this paper, the authors give a sufficient condition for pairs of functions to have a convex separator when the underlying structure is a Cartan-Hadamard manifold, or more generally: a reduced Birkhoff--Beatley system.
2
A sandwich with segment convexity
TL;DR: In this article, the authors give a sufficient condition for pairs of functions to have a convex separator when the underlying structure is a Cartan-Hadamard manifold, or more generally: a reduced Birkhoff system.
2
Convex structures induced by Chebyshev systems
Mihály Bessenyei,Bella Popovics +1 more
TL;DR: In this article, the authors characterize the combinatorial invariants of convex structures induced by Chebyshev systems and show that they are closely related to separation theorems obtained in the field of functional inequalities.
1
Axiomatic and algebraic convexity of regular pairs
TL;DR: In this paper, it was shown that two-dimensional regular pairs induce convex structures both in an axiomatic and in an algebraic way, and the aim of this note is to link these structures by showing that they coincide.
References
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