The topological versions of KKM theorem and Fan's matching theorem with applications
type: Item
instance of: scholarly article
title: The topological versions of KKM theorem and Fan's matching theorem with applications
zbMATH Open document ID: 0814.47075
DOI: 10.12775/TMNA.1993.017
author: V. Pereyra
published in: Topological Methods in Nonlinear Analysis
publication date: 1995-06-06T00:00:00Z
review text: The authors consider some versions of the KKM theorem in topological spaces without linear structures. The purpose of this paper is to obtain some more general topological types of the KKM theorem and Fan's matching theorem. As applications, the authors shall utilize the main results to study the minimax problems and the existence of solutions for a class of generalized variational inequalities. The results of this paper are not only generalizations the corresponding results of \textit{Ky Fan} [Math. Ann. 266, 519-537 (1984; Zbl 0532.47043), Math. Ann. 142, 305-310 (1961; Zbl 0093.367)], \textit{S. Park} [J. Math. Anal. Appl. 141, 164-176 (1989; Zbl 0681.47028)], \textit{C. Bardaro} and \textit{R. Ceppitelli} [J. Math. Anal. Appl. 132, 484-490 (1988; Zbl 0667.49016), J. Math. Anal. Appl. 137, 46-58 (1989; Zbl 0681.49010)], \textit{R. Bielawski} [J. Math. Anal. Appl. 127, 155-171 (1987; Zbl 0638.52002)] and \textit{F. E. Browder} [Math. Ann. 174, 285-290 (1967; Zbl 0176.452)], but also contain the main results of \textit{B.-L. Lin} and \textit{M. Geraghty} [Proc. Am. Math. Soc. 91, 377-380 (1984; Zbl 0533.90095)], \textit{B.-L. Lin} and \textit{X.-C. Quan} [J. Math. Anal. Appl. 161, 587-590 (1991; Zbl 0779.49009)] and \textit{W. Wu} [Sci. Record, New Ser. 3, 229-232 (1959; Zbl 0168.413)].
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 49J35
zbMATH DE Number: 482092
zbMATH Keywords: \(W\)-space
zbMATH Keywords: minimax theorem
zbMATH Keywords: KKM theorem in topological spaces without linear structures
zbMATH Keywords: Fan's matching theorem
reviewed by: Ulrich Kosel
MaRDI profile type: Publication
full work available at URL: tmna.1993.017
OpenAlex ID: W2587415293
description: scientific article; zbMATH DE number 482092