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ELEMENTS OF THE KKM THEORY ON CONVEX SPACES
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 Title & Authors
ELEMENTS OF THE KKM THEORY ON CONVEX SPACES
Park, Se-Hie;
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 Abstract
We introduce a new concept of convex spaces and a multimap class K having certain KKM property. From a basic KKM type theorem for a K-map defined on an convex space without any topology, we deduce ten equivalent formulations of the theorem. As applications of the equivalents, in the frame of convex topological spaces, we obtain Fan-Browder type fixed point theorems, almost fixed point theorems for multimaps, mutual relations between the map classes K and B, variational inequalities, the von Neumann type minimax theorems, and the Nash equilibrium theorems.
 Keywords
abstract convex space;generalized convex space;KKM principle;multimap (map) classes K;KC;KD;coincidence;almost fixed point;map classes ;B;
 Language
English
 Cited by
1.
COINCIDENCE THEOREMS FOR NONCOMPACT ℜℭ-MAPS IN ABSTRACT CONVEX SPACES WITH APPLICATIONS,;;

대한수학회보, 2012. vol.49. 6, pp.1147-1161 crossref(new window)
2.
APPLICATIONS OF RESULTS ON ABSTRACT CONVEX SPACES TO TOPOLOGICAL ORDERED SPACES,;

대한수학회보, 2013. vol.50. 1, pp.305-320 crossref(new window)
1.
Comments on abstract convexity structures on topological spaces, Nonlinear Analysis: Theory, Methods & Applications, 2010, 72, 2, 549  crossref(new windwow)
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APPLICATIONS OF RESULTS ON ABSTRACT CONVEX SPACES TO TOPOLOGICAL ORDERED SPACES, Bulletin of the Korean Mathematical Society, 2013, 50, 1, 305  crossref(new windwow)
3.
On the von Neumann–Sion minimax theorem in KKM spaces, Applied Mathematics Letters, 2010, 23, 10, 1269  crossref(new windwow)
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Evolution of the Minimax Inequality of Ky Fan, Journal of Operators, 2013, 2013, 1  crossref(new windwow)
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New generalizations of basic theorems in the KKM theory, Nonlinear Analysis: Theory, Methods & Applications, 2011, 74, 9, 3000  crossref(new windwow)
6.
The KKM principle in abstract convex spaces: Equivalent formulations and applications, Nonlinear Analysis: Theory, Methods & Applications, 2010, 73, 4, 1028  crossref(new windwow)
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COMMENTS ON DING'S EXAMPLES OF FC-SPACES AND RELATED MATTERS, Communications of the Korean Mathematical Society, 2012, 27, 1, 137  crossref(new windwow)
8.
COINCIDENCE THEOREMS FOR NONCOMPACT ℜℭ-MAPS IN ABSTRACT CONVEX SPACES WITH APPLICATIONS, Bulletin of the Korean Mathematical Society, 2012, 49, 6, 1147  crossref(new windwow)
9.
A Collectively Fixed Point Theorem in Abstract Convex Spaces and Its Applications, Journal of Function Spaces and Applications, 2013, 2013, 1  crossref(new windwow)
10.
Fixed Points, Maximal Elements and Equilibria of Generalized Games in Abstract Convex Spaces, Abstract and Applied Analysis, 2012, 2012, 1  crossref(new windwow)
11.
Remarks on some basic concepts in the KKM theory, Nonlinear Analysis: Theory, Methods & Applications, 2011, 74, 7, 2439  crossref(new windwow)
12.
Fixed point theory of multimaps in abstract convex uniform spaces, Nonlinear Analysis: Theory, Methods & Applications, 2009, 71, 7-8, 2468  crossref(new windwow)
13.
Remarks on Weakly KKM Maps in Abstract Convex Spaces, International Journal of Mathematics and Mathematical Sciences, 2008, 2008, 1  crossref(new windwow)
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The Fan minimax inequality implies the Nash equilibrium theorem, Applied Mathematics Letters, 2011, 24, 12, 2206  crossref(new windwow)
15.
Generalized convex spaces, L-spaces, and FC-spaces, Journal of Global Optimization, 2009, 45, 2, 203  crossref(new windwow)
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