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Applications of results on abstract convex spaces to topological ordered spaces

김훈주
대한수학회 (The Korean Mathematical Society)|2013.01|대한수학회보 (Bulletin of the KMS)|제50권 제1호|pp. 305-320

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참고문헌

키워드

abstract convex spacemaximal elementsgeneralized KKMKKM mapgeneralized γ-quasiconvexitycollectively fixed point
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초록

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..

Abstract

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..

참고문헌 (18)

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  2. C. D. Horvath, "Maximal elements and fixed points for binary relations on topological ordered spaces", J. Math. Econom, 25(3), pp.291~306 (1996)
  3. G. Kassay, "On the Knaster–Kuratowski–Mazurkiewicz and Ky fan’s theorem", Babes–Bolyai Univ. Res. Seminars Preprint, 7, pp.87~100 (1990)
  4. 김훈주, "Generalized KKM maps, maximal elements and almost fixed points", 대한수학회지, 44(2), pp.393~406 (2007), 대한수학회
  5. D. T. Luc, "Existence of solutions in variational relation problems without convexity", J. Math. Anal. Appl, 364(2), pp.544~555 (2010)
  6. Q. Luo, "KKM and Nash equilibria type theorems in topological ordered spaces", J. Math. Anal. Appl, 264(2), pp.262~269 (2001)
  7. Q. Luo, "Ky Fan’s section theorem and its applications in topological ordered spaces", Appl. Math. Lett, 17(10), pp.1113~1119 (2004)
  8. S. Park, "Another five episodes related to generalized convex spaces", Nonlinear Funct. Anal. Appl, 3, pp.1~12 (1998)
  9. S. Park, "Comments on collectively fixed points in generalized convex spaces", Appl. Math. Lett, 18(4), pp.431~437 (2005)
  10. 박세희, "Elements of the KKM theory on abstract convex spaces", 대한수학회지, 45(1), pp.1~27 (2008), 대한수학회
  11. S. Park, "Equilibrium existence theorems in KKM spaces", Nonlinear Anal, 69(12), pp.4352~4364 (2008)
  12. S. Park, "The KKM principle in abstract convex spaces: equivalent formulations and applications", Nonlinear Anal, 73(4), pp.1028~1042 (2010)
  13. S. Park, "New generalizations of basic theorems in the KKM theory", Nonlinear Anal, 74(9), pp.3000~3010 (2011)
  14. S. Park, "Admissible classes of multifunctions on generalized convex spaces", Proc. Coll. Natur. Sci. Seoul Nat. Univ, 18, pp.1~21 (1993)
  15. S. Park, "Coincidence theorems for admissible multifunctions on generalized convex spaces", J. Math. Anal. Appl, 197(1), pp.173~187 (1996)
  16. S. Park, "Foundations of the KKM theory on generalized convex spaces", J. Math. Anal. Appl, 209(2), pp.551~571 (1997)
  17. S. Park, "A unified approach to generalized KKM maps in generalized convex spaces", J. Nonlinear Convex Anal, 2(2), pp.157~166 (2001)
  18. G. Q. Tian, "Generalizations of the FKKM theorem and the Ky Fan minimax inequal- ity, with applications to maximal elements, price equilibrium, and complementarity", J. Math. Anal. Appl, 170(2), pp.457~471 (1992)

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