Uniform Convexity and Convergence of a Sequence of Sets in a Complete Geodesic Space.

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. [ABSTRACT FROM AUTHOR]