Generalized KKM Type Theorems in FC-Spaces with Applications (I) |
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Authors: | Xie Ping Ding |
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Institution: | (1) College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, 610066, P. R. China |
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Abstract: | The class KKM(X,Y) (resp., s-KKM(X,Y,Z)) of set-valued mappings with KKM (resp., s-KKM) property is introduced in FC-spaces without any convexity structure. Some generalized KKM (resp., s-KKM) type theorems are proved in FC-spaces under much weak assumptions. As applications, some new section theorems and coincidence theorems are established in FC-spaces. These theorems generalize many known results in literature. The further applications of these results will be given in a follow-up paper. |
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Keywords: | KKM (s-KKM) type theorem Transfer compactly open-valued (closed-valued) mapping Section theorem Coincidence theorems FC-space |
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