Generalized KKM Type Theorems in FC-Spaces with Applications (I)

Authors:
Xie Ping Ding
Affiliations:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu, P. R. China 610066
Venue:
Journal of Global Optimization
Year:
2006

Citing 0
Cited 3

Generalized KKM type theorems in FC-spaces with applications (II)

Journal of Global Optimization
Generalized convex spaces, L-spaces, and FC-spaces

Journal of Global Optimization
A section theorem with applications to coincidence theorems and minimax inequalities in FWC-spaces

Computers & Mathematics with Applications

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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.