A Ky Fan Matching Theorem in FC-Spaces with the Application to Minimax Inequalities

2013 ◽  
Vol 15 (3) ◽  
pp. 277
Author(s):  
Kaiting WEN
Keyword(s):  
Minimax Inequalities ◽  
Matching Theorem ◽  
Ky Fan

scholarly journals On minimax inequalities on spaces having certain contractible subsets

1993 ◽  
Vol 47 (1) ◽  
pp. 25-40 ◽  
Author(s):  
Sehie Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Minimax Theorem ◽  
Saddle Point Theorem ◽  
Minimax Inequalities ◽  
Von Neumann ◽  
Matching Theorem ◽  
Quasi Variational Inequality ◽  
Ky Fan

The concept of a convex space is extended to an H-space; that is, a space having certain family of contractible subsets. For such spaces the KKM type theorems, the Fan-Browder fixed point theorem, the Ky Fan type matching theorem, and minimax inequalities are given. Moreover, applications to a von Neumann-Sion type minimax theorem, a saddle point theorem, a quasi-variational inequality, and a Kakutani type fixed point theorem are obtained.

scholarly journals Evolution of the Minimax Inequality of Ky Fan

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Sehie Park
Keyword(s):  
Minimax Inequality ◽  
Minimax Inequalities ◽  
Long Period ◽  
Close Relationship ◽  
The Relationship ◽  
Ky Fan ◽  
Or Applications

There are quite a few generalizations or applications of the 1984 minimax inequality of Ky Fan compared with his original 1972 minimax inequality. In a certain sense, the relationship between the 1984 inequality and several hundreds of known generalizations of the original 1972 inequality has not been recognized for a long period. Hence, it would be necessary to seek such relationship. In this paper, we give several generalizations of the 1984 inequality and some known applications in order to clarify the close relationship among them. Some new types of minimax inequalities are added.

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.

scholarly journals Convex sets, fixed points, variational and minimax inequalities

1986 ◽  
Vol 34 (1) ◽  
pp. 107-117 ◽  
Author(s):  
Tzu-Chu Lin
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Convex Sets ◽  
Classical Theorem ◽  
Minimax Inequalities ◽  
Slight Extension ◽  
Ky Fan

Recently, Ky Fan extended his will known lemma (which is an extension of the classical theorem of Knaster, Kuratowski and Mazurkiewica) to the noncompact case. Using this result, another interesting lemma of Fan is generalized in this paper. As applications of our theorem, we obtain a generalizationof Browder's variational inequality and derive Fan's other recent results directly from our theorem. Also, in this paper, we give a slight extension recent results of K. K. Tan, which themselves are generalizations of many well-known results on minimax and variational inequalities.

scholarly journals A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems

1988 ◽  
Vol 45 (2) ◽  
pp. 169-183 ◽  
Author(s):  
Mau-Hsiang Shih ◽  
Kok-Keong Tan
Keyword(s):  
Fixed Point ◽  
Geometric Property ◽  
Fixed Point Theorems ◽  
Convex Sets ◽  
Minimax Inequality ◽  
Minimax Inequalities ◽  
Von Neumann ◽  
Neumann Type ◽  
Ky Fan

AbstractA geometric property of convex sets which is equivalent to a minimax inequality of the Ky Fan type is formulated. This property is used directly to prove minimax inequalities of the von Neumann type, minimax inequalities of the Fan-Kneser type, and fixed point theorems for inward and outward maps.

scholarly journals Minimax inequalities of Ky Fan

1998 ◽  
Vol 11 (6) ◽  
pp. 37-41 ◽  
Author(s):  
Ji Hui Zhang ◽  
Ruyun Ma
Keyword(s):  
Minimax Inequalities ◽  
Ky Fan

A Matching Theorem in FC-Spaces with the Application to Coincidence Questions

2012 ◽  
Vol 204-208 ◽  
pp. 4766-4770
Author(s):  
Kai Ting Wen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Coincidence Theorems ◽  
Matching Theorem ◽  
Ky Fan

A Ky Fan type matching theorem for weakly transfer compactly open valued mappings is established in FC-spaces. As applications, Fan–Browder type fixed point theorems and Ky Fan type coincidence theorems are obtained in FC-spaces.

Sign in / Sign up

Export Citation Format

Share Document