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Continuous selections and approximations in α-convex metric spaces

A. Kowalska — 2007

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

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