Geodesic
Some further applications of KKM theorem in topological semilattices
Vinh, Nguyen The1
1 Department of Mathematical Analysis, University of Transport and Communications, Hanoi, Vietnam
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 3, p. 161-173.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we obtain some further applications of KKM theorem in setting of topological semilattices such as Ky Fan-Kakutani type fixed point theorem, Sion-Neumann type set-valued minimax theorem, set-valued vector optimization problems.
DOI : 10.22436/jnsa.005.03.01
Classification : 47H10, 47H04
Keywords: generalized Ky Fan minimax inequality, set-valued mapping, topological semilattices, \(C_\Delta\)-quasiconvex, upper (lower) \(C\)-continuous, fixed point, Nash equilibrium.

Vinh, Nguyen The 1

1 Department of Mathematical Analysis, University of Transport and Communications, Hanoi, Vietnam 
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Vinh, Nguyen The. Some further applications of KKM theorem in topological semilattices. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 3, p. 161-173. doi : 10.22436/jnsa.005.03.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.03.01/

[1] Berge, C. Espaces Topologiques, Fonctions Multivoques, Dunnod, Paris, 1959

[2] Blum, E.; Oettli, W. From optimization and variational inequalities to equilibrium problems, Math. Student, Volume 63 (1994), pp. 123-145

[3] Deguire, P.; Lassonde, M. Familles sélectantes , Topol. Methods Nonlinear Anal., Volume 5 (1995), pp. 261-269

[4] K. Fan A minimax inequality and applications, In, O. Shisha, ed., Inequalities III, Proceedings of the third Symposium on inequalities, Academic Press, New York, 1972

[5] Horvath, C. D. Contractibility and Generalized Convexity, J. Math. Anal. Appl. , Volume 156 (1991), pp. 341-357

[6] Horvath, C. D.; Ciscar, J. V. Llinares Maximal elements and fixed points for binary relations on topological ordered spaces , J. Math. Econom. , Volume 25 (1996), pp. 291-306

[7] Kelly, J. L. General Topology , Van Nostrand, Princeton, NJ, 1955

[8] Lin, L.-J.; Tan, N. X. On quasivariational inclusion problems of type I and related problems, J. Glob. Optim. , Volume 39 (2007), pp. 393-407

[9] Luc, D. T. Theory of Vector Optimization, In, Lecture Notes in Economics and mathematical systems, Vol. 319, Springer-Verlag, Berlin, 1989

[10] Luo, Q. KKM and Nash equilibria type theorems in topological ordered spaces, J. Math. Anal. Appl., Volume 264 (2001), pp. 262-269

[11] Luo, Q. The applications of the Fan-Browder fixed point theorem in topological ordered spaces, Appl. Math. Lett. , Volume 19 (2006), pp. 1265-1271

[12] Peng, J. W.; Yang, X. M. On existence of a solution for the system of generalized vector quasi-equilibrium problems with upper semicontinuous set-valued maps, Inter. J. Math. Math. Sciences , Volume 15 (2005), pp. 2409-2420

[13] R. R. Phelps Convex functions, monotone operators and differentiablity, Lecture Notes in Mathematics, Springer- Verlag, Vol. 1364, 1989

[14] Tan, K.-K.; Zhang, X.-L. Fixed point theorems on G-convex spaces and applications, Proc. Nonlinear Func. Anal. Appl. , Volume 1 (1996), pp. 1-19

[15] Tychonoff, A. Ein Fixpunktsatz, Math. Ann. , Volume 111 (1935), pp. 767-776

[16] Vinh, N. T. Matching theorems, fixed point theorems and minimax inequalities in topological ordered spaces, Acta Math. Vietnam. , Volume 30 (2005), pp. 211-224

[17] Vinh, N. T. Some generalized quasi-Ky Fan inequalities in topological ordered spaces, Vietnam J. Math., Volume 36 (2008), pp. 437-449

[18] Vinh, N. T. Systems of generalized quasi-Ky Fan inequalities and Nash equilibrium points with set-valued maps in topological semilattices , PanAmer. Math. J. , Volume 19 (2009), pp. 79-92

[19] Yuan, G. X. Z. KKM Theory and Applications in Nonlinear Analysis, Marcel Dekker Inc., New York, 1999

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