A systematization of convexity concepts for sets and functions.

Breckner, Wolfgang W.; Kassay, Gábor

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A note on the convexity theorem for mean values of subtemperatures.

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There are many types of midconvexities, for example Jensen convexity, t-convexity, (s,t)-convexity. We provide a uniform framework for all the above mentioned midconvexities by considering a generalized middle-point map on an abstract space X. We show that we can define and study the basic convexity properties in this setting.

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A Generalization of m-Convexity and a Sandwich Theorem

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Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.