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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc99-0-13,
author = {Jacek Tabor and J\'ozef Tabor and Krzysztof Misztal},
title = {Generalized midconvexity},
journal = {Banach Center Publications},
volume = {99},
year = {2013},
pages = {207-215},
zbl = {1285.26023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc99-0-13}
}
Jacek Tabor; Józef Tabor; Krzysztof Misztal. Generalized midconvexity. Banach Center Publications, Tome 99 (2013) pp. 207-215. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc99-0-13/