Fixed point theorems and vector valued minimax theorems
type: Item
instance of: scholarly article
title: Fixed point theorems and vector valued minimax theorems
zbMATH Open document ID: 0698.49011
DOI: 10.1016/0022-247X(90)90308-3
author: Carlo Bardaro
author: Rita Ceppitelli
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The objective of this paper is the study of the following minimax relation: \[ \sup_{x\in X}\inf_{y\in Y}f(x,y)=\inf_{y\in Y}\sup_{x\in X}f(x,y) \] in a general setting, namely without convexity and compactness assumptions. Here, f: \(X\times Y\to E\) is a function with values in a partially ordered vector space and X,Y are topological spaces with a structure of H-space (a merely topological generalization of convexity). In order to show these minimax theorems, some H-space versions of fixed point theorems are proved which extend some previous results by \textit{K. Fan} [Inequalities III, Proc. 3rd Symp., Los Angeles 1969, 103-113 (1972; Zbl 0302.49019)] and \textit{M. Lassonde} [J. Math. Anal. 97,151-201 (1983; Zbl 0527.47037)].
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 4144814
zbMATH Keywords: H-space
zbMATH Keywords: fixed point theorems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4144814