GENERALIZATIONS OF SOME KKM TYPE RESULTS ON HYPERBOLIC SPACES

Abstract

In some previous works, it is known that the KKM type results on Hadamard manifolds can be extended to hyperbolic spaces originated from Kirk in 1982 and Reich- Shafrir in 1990. Such results are the KKM theorem, the Fan-Browder fixed point theorem, Nash equilibrium theorem, variational inequalities, etc. based on our theory of abstract convex spaces. In the present article, we show that our method can be applied some recent works on Hadamard manifolds. Historical remarks are added on the study of the KKM type results on Hadamard manifolds and hyperbolic spaces.