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

Mau-Hsiang Shih, Kok-Keong Tan

Type: Article

Publication Date: 1988-10-01

Citations: 22

DOI: https://doi.org/10.1017/s144678870003007x

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Abstract

Abstract A 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.

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Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics - View - PDF

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Citing (15)

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+	A remark on Ky fan's minimax principle	2008	Haı̈m Brezis Louis Nirenberg G. Stampacchia
+	Comparison Theorems on Minimax Inequalities, Variational Inequalities, and Fixed Point Theorems	1983	Kok-Keong Tan
+	On general minimax theorems	1958	Maurice Sion
+	Extensions of two fixed point theorems of F. E. Browder	1970	Ky Fan
+ PDF Chat	A fixed-point theorem for inward and outward maps	1968	Benjamin Halpern George M. Bergman
+ PDF Chat	Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces	1952	Ky Fan
+	On a sharpened form of the Schauder fixed-point theorem	1977	Felix E. Browder
+ PDF Chat	Nonlinear variational inequalities and fixed point theorems	1976	Wataru Takahashi
+ PDF Chat	A minimax inequality and its applications to variational inequalities	1981	Chi-Lin Yen
+	The fixed point theory of multi-valued mappings in topological vector spaces	1968	Felix E. Browder
+	A generalization of Tychonoff's fixed point theorem	1961	Ky Fan
+	Some properties of convex sets related to fixed point theorems	1984	Ky Fan
+	Existence theorems and extreme solutions for inequalities concerning convex functions or linear transformations	1957	Ky Fan
+	A new generalization of the Schauder fixed point theorem	1967	Felix E. Browder
+	Extensions of two fixed point theorems of F. E. Browder	1969	Ky Fan