On minimax inequalities in topological spaces without convexity structure

• Autorzy: Lu H.-S.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we give a new nonempty intersection theorem in general topological spaces without convexity structure. As its applications, some new minimax inequalities are obtained in general topological spaces without convexity structure.

Słowa kluczowe

EN

intersection theorem; minimax inequality; transfer compactly closed-valued; transfer compactly open-valued; acyclic set; set-valued mapping

PL

klasa multifunkcji

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2007
• Tom: Vol. 13, nr 1
• Strony: 133--149
• Opis fizyczny: Bibliogr. poz 17

Twórcy

autor

Lu H.-S.

• School of Economics and Management. Jiangsu Teachers University of Technology, Changzhou 213001, People's republic of China,

Bibliografia

• [1] Aubin, J.P., Ekeland, I., Applied Nonlinear Analysis, John Wiley & Sons, New York, 1984.
• [2] Bardaro, C., Ceppitelli, R., Some further generalizations of Knaster-Kuratowski-Mazurkiewics theorem and minimax inequalities, J. Math. Anal. Appl. 132(3) (1988), 484-490.
• [3] Ding, X. P., Generalized G- K K M theorems in genemlized convex spaces and their applications, J. Math. Anal. Appl. 266 (2002), 21-37.
• [4] Fan, K., A genemlization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305-310.
• [5] Fan, K., Some properties of convex sets relation to fixed point theorems, Math. Ann. 266 (1984), 519-537.
• [6] Granas, A., Liu, F. C., Coincidence for set-valued maps and minimax inequalities, J. Math. Pures Appl. (9) 65 (1984), 119-148.
• [7] Ha, C. W., Minimax and fixed point theorems, Math. Ann. 248 (1980), 73-77.
• [8] Ha, C. W., On a minimax inequality of Ky Fan, Proc. Amer. Math. Soc. 99 (1987), 680-682.
• [9] Lu, H. S., Tang, D. S., An intersection theorem in L-convex spaces with applications, J. Math. Anal. Appl. 312 (2005), 343-356.
• [10] Lu, H. s., Zhang, J. H., Minimax inequalities in the spaces without linear structure, Taiwanese J. Math. 8(4) (2004),703-712.
• [11] McClendon, J. F., Minimax and variational inequalities for compact spaces, Proc. Amer. Math. Soc. 89(4) (1983),717-721.
• [12] Shioji, N., A further generalization of Knaster-Kuratowski-Mazurkiewics theorem, Proc. Amer. Math. Soc. 117 (1991),187-195.
• [13] Tarafdar , E., Fixed-point theorems in H -spaces and equilibrium point of abstmct economies, J. Austral. Math. Soc. Ser. A 53 (1992), 252-260.
• [14] Tarafdar, E., Watson, P. J., A coincidence point theorem and related results, Appl. Math. Lett. 11(1) (1998), 37-40.
• [15] Tian, G. Q., Genemlization of FKKM theorem and the Ky Fan minimax inequality with applications to maximal elements, price equilibrium and complementarity, J. Math. Anal. Appl. 170 (1992),457-471.
• [16] Zhang, J .H., Ma, R. Y., Minimax inequalities of Ky Fan, Appl. Math. Lett. 11 (1998), 37-41.
• [17] Zhang, J. H., Some minimax inequalities for mappings with noncompact domain, Appl. Math. Lett. 17 (2004),717-720.