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http://dx.doi.org/10.14403/jcms.2012.25.2.227

A TOPOLOGICAL MINIMAX INEQUALITY WITH ${\gamma}$-DCQCV AND ITS APPLICATIONS  

Kim, Won Kyu (Department of Mathematics Education Chungbuk National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.25, no.2, 2012 , pp. 227-233 More about this Journal
Abstract
In this paper, using the ${\gamma}$-diagonally $\mathcal{C}$-quasiconcave condition, we will prove a new minimax inequality in a non-convex subset of a topological space which generalizes Fan's minimax inequality and its generalizations in several aspects.
Keywords
${\gamma}$-diagonally $\mathcal{C}$-quasiconcave; minimax inequality;
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1 K. Fan, Fixed point and minimax theorems in locally convex topological linear spaces. Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 121-126.   DOI   ScienceOn
2 K. Fan, Minimax theorems. Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 42-47.   DOI   ScienceOn
3 K. Fan, A Minimax inequality and applications, In Inequalities III (Edited by O. Shisha) Proc. of 3rd Symposium on Inequalities, 103-113, Academic Press, New York, 1972.
4 W. K. Kim, Generalized C-concave Conditions and Their Applications, Acta Math. Hungarica 130 (2010), 140-154.
5 S.-S. Chang and Y. Zhang, Generalized KKM theorem and variational inequal- ities, J. Math. Anal. Appl. 159 (1991), 208-223.   DOI
6 J. Zhou and G. Chen, Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities, J. Math. Anal. Appl. 132 (1988), 213-225.   DOI
7 W. K. Kim and K. H. Lee, On the existence of Nash equilibrium in N-person games with C-concavity, Computers & Math. Appl. 44 (2002), 1219-1228.   DOI   ScienceOn
8 K.-K. Tan, Comparison theorems on minimax inequalities, variational inequal- ities and fixed point theorems, J. London Math. Soc. 28 (1983), 555-562.
9 G.-S. Tang, C.-Z. Cheng and B.-L. Lin, Some generalized Ky Fan's inequalities, Taiwanese J. Math. 13 (2009), 239-251.   DOI
10 J. von Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann. 100 (1928), 295-320.   DOI