Evolution of the 1984 KKM theorem of Ky Fan. (English) Zbl 1475.47026
Summary: Recently we established the Knaster, Kuratowski, and Mazurkiewicz (KKM) theory on abstract convex spaces. In our research, we noticed that there are quite a few generalizations and applications of the 1984 KKM theorem of Ky Fan compared with his celebrated 1961 KKM lemma. In a certain sense, the relationship between the 1984 theorem and hundreds of known generalizations of the original KKM theorem has not been recognized for a long period. There would be some reasons to explain this fact. Instead, in this paper, we give several generalizations of the 1984 theorem and some known applications in order to reveal the close relationship among them.
MSC:
| 47H04 | Set-valued operators |
Keywords:
KKM theorem; Fan’s 1961 KKM lemma; 1984 KKM theorem; convex space; H-space; \(G\)-convex space; \(\phi_A\)-space; (partial) KKM space; abstract convex spaceReferences:
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