scholarly journals A minimax inequality with applications to existence of equilibrium point and fixed point theorems

1992 ◽  
Vol 63 (2) ◽  
pp. 233-247 ◽  
Author(s):  
Xie Ding ◽  
Kok-Keong Tan
Keyword(s):  
Fixed Point ◽  
Equilibrium Point ◽  
Fixed Point Theorems ◽  
Minimax Inequality ◽  
Existence Of Equilibrium

scholarly journals A G-KKM type theorem and its applications to minimax inequalities on G-convex spaces

1998 ◽  
Vol 11 (4) ◽  
pp. 493-505 ◽  
Author(s):  
Mohammad S. R. Chowdhury
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Type Theorem ◽  
Minimax Inequality ◽  
Compact Sets ◽  
Minimax Inequalities ◽  
Special Cases ◽  
Convex Spaces

A G-KKM type theorem is obtained on G-convex spaces. As application, a generalization of Ky Fan's minimax inequality to non-compact sets on G-convex spaces is first obtained. As special cases of this minimax inequality, some new minimax inequalites are obtained. Four fixed point theorems and four equivalent formulations of the second minimax inequality are also obtained.

scholarly journals A new minimax inequality on H-spaces with applications

1990 ◽  
Vol 41 (3) ◽  
pp. 457-473 ◽  
Author(s):  
Xie Ping Ding ◽  
Won Kyu Kim ◽  
Kok-Keong Tan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Minimax Theorem ◽  
Minimax Inequality ◽  
Minimax Inequalities ◽  
Convex Inequalities ◽  
Systems Of Inequalities ◽  
System Of Inequalities

A new minimax inequality on H-spaces is obtained together with six equivalent formulations. As applications, some results on fixed point theorems and system of inequalities are proved. Our results generalise the corresponding results on (1) minimax inequalities due to Fan, Yen, Tan, Shih-Tan and Ding-Tan, (2) fixed point theorems due to Browder, Tarafdar, Shih-Tan and Ding-Tan, (3) convex inequalities due to Fan, (4) systems of inequalities due to Granas-Liu and (5) a minimax theorem due to Kneser.

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 Fixed point theorems in H-spaces and equilibrium points of abstract economies

1992 ◽  
Vol 53 (2) ◽  
pp. 252-260 ◽  
Author(s):  
E. Tarafdar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Equilibrium Points ◽  
Existence Of Equilibrium ◽  
Abstract Economies ◽  
Commodity Space ◽  
Abstract Economics

AbstractSome fixed point theorems on H-spaces are presented. These theorems are then applied to generalize a theorem of Fan concerning sets with convex sections to H-spaces and to prove the existence of equilibrium points of abstract economics in which the commodity space is an H-space.

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