Some applications of the Knaster-Kuratowski and Masurkiewicz principle in hyperconvex metric spaces
In this paper, as applications of the Knaster-Kuratowski and Mazurkiewicz principle in the hyperconvex version, we obtain the Ky Fan type matching theorems for closed and open covers. As applications, some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath, and Lassonde are established. Then, the Ky Fan type best approximation theorem and Schauder-Tychonoff fixed-point theorem (i.e., Fan-Glicksberg fixed-point theorem) for set-valued mappings in noncompact hyperconvex spaces are also given. Finally, we obtain a general form of the Browder-Fan fixed-point theorem for set-valued mappings in noncompact hyperconvex spaces. These results include corresponding results in the literature as special cases. (C) 2000 Elsevier Science Ltd. All rights reserved.
hyperconvex space admissible set generalized metric fan-kkm mapping non-compactness measure dual form of fan-kkm principle ky fan matching theorem browder-fan fixed point schauder-tychonoff fixed point fan-glicksberg fixed point and best approximation