Geodesic
Continuous selections and approximations in α-convex metric spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 27 (2007) no. 2, pp. 265-294.

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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.
Keywords: generalized convexity, selections, relative selections, graph-approximations 
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Kowalska, A. Continuous selections and approximations in α-convex metric spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 27 (2007) no. 2, pp. 265-294. http://geodesic.mathdoc.fr/item/DMDICO_2007_27_2_a2/

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