Some nonempty intersection theorems in generalized interval spaces with applications
type: Item
instance of: scholarly article
title: Some nonempty intersection theorems in generalized interval spaces with applications
zbMATH Open document ID: 0864.54040
author: Shiyi Cao
author: Xian Wu
author: Shihsen Chang
author: Dacheng Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-06-22T00:00:00Z
review text: A generalized interval space is defined and a parametric type of KKM theorems in generalized interval spaces are established. These results are applied to prove minimax theorems which contain results of Cheng and Lin, Lin and Quan, Brézis, Nirenberger and Stampacchia, Komornik, M. A. Geraghry and Lin, Stachó and Wu. They also include the famous von Neumann theorem. These results are also applied to the section problem and to variational inequality problems. They extend Ky Fan's famous theorem for implicit variational inequalities and Theorem 2 of Yen to the case of generalized interval spaces. Recently, \textit{B. Thompson} and \textit{X.-Z. Yuan} established topological intersection theorems for two set-valued mappings in [Numer. Funct. Anal. Optimization 17, 437-452 (1996; Zbl 0854.49009)]. But the results are quite different.
reviewed by: Lai-Jiu Lin
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 902575
zbMATH Keywords: generalized interval spaces
zbMATH Keywords: minimax theorems
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0176
OpenAlex ID: W2073146887
DOI: 10.1006/JMAA.1996.0176
description: scientific article; zbMATH DE number 902575