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Uniform convexity and convergence of a sequence of sets in a complete geodesic space. (English) Zbl 1506.46056

Summary: In this paper, we first introduce two new notions of uniform convexity on a geodesic space, and we prove their properties. Moreover, we reintroduce a concept of the set-convergence in complete geodesic spaces, and we prove a relation between the metric projections and the convergence of a sequence of sets.

MSC:

46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54E50 Complete metric spaces
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