In this paper we propose a definition of generalized KnasterKuratowski-Mazurkiewicz mappings to encompass R-KKM mappings [5], L-KKM mappings [11], T-KKM mappings [18, 19], and many recent existing mappings. Knaster-KuratowskiMazurkiewicz type theorems are established in general topological spaces to generalize known results. | 131 TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 20, SỐ K2-2017 Generalized Knaster-Kuratowski-Mazurkiewicz type theorems and applications to minimax inequalities Ha Manh Linh Abstract— Knaster-Kuratowski-Mazurkiewicz type theorems play an important role in nonlinear analysis, optimization, and applied mathematics. Since the first well-known result, many international efforts have been made to develop sufficient conditions for the existence of points intersection (and their applications) in increasingly general settings: Gconvex spaces [21, 23], L-convex spaces [12], and FCspaces [8, 9]. Applications of Knaster-Kuratowski-Mazurkiewicz type theorems, especially in existence studies for variational inequalities, equilibrium problems and more general settings have been obtained by many authors, see . recent papers [1, 2, 3, 8, 18, 24, 26] and the references therein. In this paper we propose a definition of generalized KnasterKuratowski-Mazurkiewicz mappings to encompass R-KKM mappings [5], L-KKM mappings [11], T-KKM mappings [18, 19], and many recent existing mappings. Knaster-KuratowskiMazurkiewicz type theorems are established in general topological spaces to generalize known results. As applications, we develop in detail general types of minimax theorems. Our results are shown to improve or include as special cases several recent ones in the literature Index Terms— L - T -KKM mappings, Generalized convexity, Transfer compact semicontinuity, Minimax theorems, Saddle-points. 1 INTRODUCTION E xistence of solutions takes a central place in the optimization theory. Studies of the existence of solutions of a problem are based on existence results for important points in nonlinear analysis like fixed points, maximal points, intersection points, etc. Manuscript Received on July 13th, 2016. Manuscript Revised December 06th, 2016. This work was supported by University of Information Technology, Vietnam National University Hochiminh City under grant number D1-2017-07. Ha Manh .
