The Knaster--Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications (Q1961314)

The authors give a characterization of the Knaster--Kuratowski--Mazurkiewicz principle in hyperconvex metric spaces. As applications, they give hyperconvex versions of Fan's minimax principle and Fan's best approximation theorem for set-valued mappings. In particular, the Browder--Fan and Schauder--Tychonoff fixed point theorems are extended in hyperconvex metric spaces. Finally, existence theorems for saddle points, intersection theorems and Nash equilibria in hyperconvex metric spaces are obtained.