In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1085,
author = {A. Kowalska},
title = {Continuous selections and approximations in $\alpha$-convex metric spaces},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {27},
year = {2007},
pages = {265-294},
zbl = {1146.54009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1085}
}
A. Kowalska. Continuous selections and approximations in α-convex metric spaces. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 27 (2007) pp. 265-294. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1085/
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