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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Ding, X.P. Generalized KKM Type Theorems in FC-Spaces with Applications (I). J Glob Optim 36, 581–596 (2006). https://doi.org/10.1007/s10898-006-9028-x
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DOI: https://doi.org/10.1007/s10898-006-9028-x