A Note on König and Close Convexity in Minimax Theorems

2016 ◽  
Vol 170 (1) ◽  
pp. 65-71
Author(s):  
Fernando Luque-Vásquez ◽  
J. Adolfo Minjárez-Sosa ◽  
Max E. Mitre-Báez
Keyword(s):  
Minimax Theorems

scholarly journals Topological minimax theorems

1984 ◽  
Vol 91 (3) ◽  
pp. 377-377 ◽  
Author(s):  
Michael A. Geraghty ◽  
Bor-Luh Lin
Keyword(s):  
Minimax Theorems

scholarly journals Generalized Knaster-Kuratowski-Mazurkiewicz type theorems and applications to minimax inequalities

2017 ◽  
Vol 20 (K2) ◽  
pp. 131-140
Author(s):  
Linh Manh Ha
Keyword(s):  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Applied Mathematics ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Minimax Theorems ◽  
Minimax Inequalities ◽  
Special Cases ◽  
Kkm Mappings ◽  
Definition Of

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 e.g. 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.

Minimax Theorems

1996 ◽  
Author(s):  
Michel Willem
Keyword(s):  
Minimax Theorems
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