대한수학회지 (Journal of the Korean Mathematical Society)

  • 제45권1호
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  • Pages.1-27
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  • 2008
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ELEMENTS OF THE KKM THEORY ON CONVEX SPACES

  • Park, Se-Hie (The National Academy of Sciences, Department of Mathematical Sciences Seoul National University)
  • 발행 : 2008.01.31
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초록

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.

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참고문헌

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피인용 문헌

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  2. Fixed Points, Maximal Elements and Equilibria of Generalized Games in Abstract Convex Spaces vol.2012, 2012, https://doi.org/10.1155/2012/842515
  3. New generalizations of basic theorems in the KKM theory vol.74, pp.9, 2011, https://doi.org/10.1016/j.na.2011.01.020
  4. The KKM principle in abstract convex spaces: Equivalent formulations and applications vol.73, pp.4, 2010, https://doi.org/10.1016/j.na.2010.04.029
  5. Generalized convex spaces, L-spaces, and FC-spaces vol.45, pp.2, 2009, https://doi.org/10.1007/s10898-008-9363-1
  6. A Collectively Fixed Point Theorem in Abstract Convex Spaces and Its Applications vol.2013, 2013, https://doi.org/10.1155/2013/517469
  7. The Fan minimax inequality implies the Nash equilibrium theorem vol.24, pp.12, 2011, https://doi.org/10.1016/j.aml.2011.06.027
  8. COMMENTS ON DING'S EXAMPLES OF FC-SPACES AND RELATED MATTERS vol.27, pp.1, 2012, https://doi.org/10.4134/CKMS.2012.27.1.137
  9. Comments on abstract convexity structures on topological spaces vol.72, pp.2, 2010, https://doi.org/10.1016/j.na.2009.06.100
  10. Remarks on some basic concepts in the KKM theory vol.74, pp.7, 2011, https://doi.org/10.1016/j.na.2010.10.035
  11. Fixed point theory of multimaps in abstract convex uniform spaces vol.71, pp.7-8, 2009, https://doi.org/10.1016/j.na.2009.01.081
  12. COINCIDENCE THEOREMS FOR NONCOMPACT ℜℭ-MAPS IN ABSTRACT CONVEX SPACES WITH APPLICATIONS vol.49, pp.6, 2012, https://doi.org/10.4134/BKMS.2012.49.6.1147
  13. On the von Neumann–Sion minimax theorem in KKM spaces vol.23, pp.10, 2010, https://doi.org/10.1016/j.aml.2010.06.011
  14. Remarks on Weakly KKM Maps in Abstract Convex Spaces vol.2008, 2008, https://doi.org/10.1155/2008/423596
  15. Evolution of the Minimax Inequality of Ky Fan vol.2013, 2013, https://doi.org/10.1155/2013/124962
  16. Fixed point theorems and $$L^{*}$$L∗-operators vol.20, pp.1, 2018, https://doi.org/10.1007/s11784-018-0494-9
  17. Applications of some basic theorems in the KKM theory vol.2011, pp.1, 2011, https://doi.org/10.1186/1687-1812-2011-98
  18. Evolution of the 1984 KKM theorem of Ky Fan vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1812-2012-146