REMARKS ON THE KKM THEORY OF HADAMARD MANIFOLDS AND HYPERBOLIC SPACES

Abstract

In 2012, Yang and Pu [Indian J. Pure Appl. Math., 43(2) (2012), 129–144] proved an Browder type fixed point theorem on Hadamard manifolds with strongly geodesic convexity. In this paper, we show that their main results can be obtained from the one in the more general spaces. As applications, we claim that their maximal element theorems, section theorems, Ky Fan type minimax inequality, and equilibrium theorem about non-cooperative games on Hadamard manifold are already obtained in some sense.