scholarly journals On Minimax Inequalities in Topological Spaces Without Convexity Structure

2007 ◽  
Vol 13 (1) ◽  
Author(s):  
H.-S. Lu
Keyword(s):  
Topological Spaces ◽  
Minimax Inequalities ◽  
Convexity Structure

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.

scholarly journals Existence of Equilibria for Discontinuous Games in General Topological Spaces with Binary Relations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ji-Cheng Hou
Keyword(s):  
Topological Spaces ◽  
Discontinuous Games ◽  
Binary Relations ◽  
Preference Relations ◽  
Convexity Structure ◽  
Existence Of Equilibria

We provide several results on the existence of equilibria for discontinuous games in general topological spaces without any convexity structure. All of the theorems yielding existence of equilibria here are stated in terms of the player’s preference relations over joint strategies.

scholarly journals A New Fixed Point Theorem and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Min Fang ◽  
Xie Ping Ding
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Topological Space ◽  
Point Theorem ◽  
Kkm Theorem ◽  
Minimax Inequalities ◽  
Convexity Structure ◽  
Ky Fan

A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space) without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.

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