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.


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
Full Text: DOI


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