Coincidence Theorems with Applications to Minimax Inequalities, Section Theorem, Best Approximation and Multiobjective Games in Topological Spaces

2006 ◽  
Vol 22 (6) ◽  
pp. 1809-1818 ◽  
Author(s):  
Lei Deng ◽  
Ming Ge Yang
Keyword(s):  
Best Approximation ◽  
Topological Spaces ◽  
Minimax Inequalities ◽  
Coincidence Theorems ◽  
Section Theorem

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 Coincidence theorems and minimax inequalities in abstract convex spaces

2011 ◽  
Vol 2011 (1) ◽  
pp. 126 ◽  
Author(s):  
Yeol Je Cho ◽  
Mohsen Delavar ◽  
Seyed Mohammadzadeh ◽  
Mehdi Roohi
Keyword(s):  
Minimax Inequalities ◽  
Coincidence Theorems ◽  
Convex Spaces

scholarly journals Extensions of best approximation and coincidence theorems

1997 ◽  
Vol 20 (4) ◽  
pp. 689-698 ◽  
Author(s):  
Sehie Park
Keyword(s):  
Continuous Function ◽  
Vector Space ◽  
Topological Vector Space ◽  
Compact Space ◽  
Best Approximation ◽  
Upper Semicontinuous ◽  
Coincidence Theorems ◽  
Continuous Seminorm ◽  
Upper Semicontinuous Multifunction

LetXbe a Hausdorff compact space,Ea topological vector space on whichE*separates points,F:X→2Ean upper semicontinuous multifunction with compact acyclic values, andg:X→Ea continuous function such thatg(X)is convex andg−1(y)is acyclic for eachy∈g(X). Then either (1) there exists anx0∈Xsuch thatgx0∈Fx0or (2) there exist an(x0,z0)on the graph ofFand a continuous seminormponEsuch that0<p(gx0−z0)≤p(y−z0)         for all         y∈g(X). A generalization of this result and its application to coincidence theorems are obtained. Our aim in this paper is to unify and improve almost fifty known theorems of others.

scholarly journals New generalisations of an H-KKM type theorem and their applications

1993 ◽  
Vol 48 (3) ◽  
pp. 451-464 ◽  
Author(s):  
Xie Ping Ding
Keyword(s):  
Type Theorem ◽  
Minimax Inequalities ◽  
Geometric Properties ◽  
Coincidence Theorems ◽  
Abstract Setting ◽  
Ky Fan

In this note, we establish some new generalisations of an H-KKM type theorem which unify and generalise the corresponding results of Horvath, Bardaro-Ceppitelli, Tarafdar, Shioji, Park and others. As applications of our H-KKM type principle, we obtain some new generalisations of the Ky Fan type geometric properties of. H-spaces, minimax inequalities and coincidence theorems in Horvath's abstract setting.

Sign in / Sign up

Export Citation Format

Share Document