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APPLICATIONS OF RESULTS ON ABSTRACT CONVEX SPACES TO TOPOLOGICAL ORDERED SPACES
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 Title & Authors
APPLICATIONS OF RESULTS ON ABSTRACT CONVEX SPACES TO TOPOLOGICAL ORDERED SPACES
Kim, Hoonjoo;
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 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..
 Keywords
abstract convex space;KKM map;generalized KKM;generalized;-quasiconvexity;maximal elements;topological semilattices with path-connected intervals;collectively fixed point;
 Language
English
 Cited by
 References
1.
Q. H. S. Al-Homidan, Q. H. Ansari, and J. C. Yao, Collectively fixed point and maximal element theorems in topological semilattice spaces, Appl. Anal. 90 (2011), no. 6, 865-888. crossref(new window)

2.
C. D. Horvath and J. V. L. Ciscar, Maximal elements and fixed points for binary relations on topological ordered spaces, J. Math. Econom. 25 (1996), no. 3, 291-306. crossref(new window)

3.
G. Kassay and I. Kolumban, On the Knaster-Kuratowski-Mazurkiewicz and Ky fan's theorem, Babes-Bolyai Univ. Res. Seminars Preprint 7 (1990), 87-100.

4.
H. Kim and S. Park, Generalized KKM maps, maximal elements and almost fixed points, J. Korean Math. Soc. 44 (2007), no. 2, 393-406. crossref(new window)

5.
D. T. Luc, E. Sarabi, and A. Soubeyran, Existence of solutions in variational relation problems without convexity, J. Math. Anal. Appl. 364 (2010), no. 2, 544-555. crossref(new window)

6.
Q. Luo, KKM and Nash equilibria type theorems in topological ordered spaces, J. Math. Anal. Appl. 264 (2001), no. 2, 262-269. crossref(new window)

7.
Q. Luo, Ky Fan's section theorem and its applications in topological ordered spaces, Appl. Math. Lett. 17 (2004), no. 10, 1113-1119. crossref(new window)

8.
S. Park, Another five episodes related to generalized convex spaces, Nonlinear Funct. Anal. Appl. 3 (1998), 1-12.

9.
S. Park, Comments on collectively fixed points in generalized convex spaces, Appl. Math. Lett. 18 (2005), no. 4, 431-437. crossref(new window)

10.
S. Park, Elements of the KKM theory on abstract convex spaces, J. Korean Math. Soc. 45 (2008), no. 1, 1-27. crossref(new window)

11.
S. Park, Equilibrium existence theorems in KKM spaces, Nonlinear Anal. 69 (2008), no. 12, 4352-4364. crossref(new window)

12.
S. Park, The KKM principle in abstract convex spaces: equivalent formulations and applications, Nonlinear Anal. 73 (2010), no. 4, 1028-1042. crossref(new window)

13.
S. Park, New generalizations of basic theorems in the KKM theory, Nonlinear Anal. 74 (2011), no. 9, 3000-3010. crossref(new window)

14.
S. Park and H. Kim, Admissible classes of multifunctions on generalized convex spaces, Proc. Coll. Natur. Sci. Seoul Nat. Univ. 18 (1993), 1-21.

15.
S. Park and H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996), no. 1, 173-187. crossref(new window)

16.
S. Park and H. Kim, Foundations of the KKM theory on generalized convex spaces, J. Math. Anal. Appl. 209 (1997), no. 2, 551-571. crossref(new window)

17.
S. Park and W. Lee, A unified approach to generalized KKM maps in generalized convex spaces, J. Nonlinear Convex Anal. 2 (2001), no. 2, 157-166.

18.
G. Q. Tian, Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity, J. Math. Anal. Appl. 170 (1992), no. 2, 457-471. crossref(new window)