New Characterization of Geodesic Convexity on Hadamard Manifolds with Applications

Abstract

In this paper, some new results, concerned with the geodesic convex hull and geodesic convex combination, are given on Hadamard manifolds. An S-KKM theorem on a Hadamard manifold is also given in order to generalize the KKM theorem. As applications, a Fan---Browder-type fixed point theorem and a fixed point theorem for the a new mapping class are proved on Hadamard manifolds.