Some applications of the KKM-mapping principle in hyperconvex metric spaces

Abstract

In 1996 Khamsi proved a result in hyperconvex metric spaces which is an analogue of the famous KKM-maps principle proved by Ky Fan in 1972 for topological vector spaces. In this note, using the above result due to Khamsi, we establish two results in hyperconvex metric spaces which are analogues of the famous Ky Fan inequality and Sion minimax theorem proved for topological vector spaces in 1972 and 1958, respectively.