Applications of some basic theorems in the KKM theory

In this review, we introduce a new KKM-type theorem for intersectionally closed-valued KKM map on abstract convex spaces and its direct consequences such as a Fan-Browder-type fixed point theorem and maximal element theorems. For these basic theorems of the KKM theory, we review previously obtained...

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Bibliographic Details
Published inFixed point theory and applications (Hindawi Publishing Corporation) Vol. 2011; no. 1; p. 98
Main Author Park, Sehie
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 07.12.2011
BioMed Central Ltd
Subjects
Analysis
Applications of Mathematics
Differential Geometry
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
S. Park's Contribution to the Development of Fixed Point Theory and KKM Theory
Topology
KKM-type theorem
intersectionally closed
unionly open
abstract convex space
fixed point
maximal element
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Summary:In this review, we introduce a new KKM-type theorem for intersectionally closed-valued KKM map on abstract convex spaces and its direct consequences such as a Fan-Browder-type fixed point theorem and maximal element theorems. For these basic theorems of the KKM theory, we review previously obtained particular consequences of them mainly due to the author and their recent applications obtained by other authors. Therefore, those applications might be improved by following our new results. 2010 Mathematics Subject Classification: 47H04; 47H10; 52A99; 54H25; 55M20; 58E35; 90D13.
ISSN:1687-1812
1687-1812
DOI:10.1186/1687-1812-2011-98