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Generalized midconvexity

Jacek Tabor; Józef Tabor; Krzysztof Misztal — 2013

Banach Center Publications

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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