Generalized KKM-type theorems for weakly generalized KKM mapping with some applications
type: Item
instance of: scholarly article
title: Generalized KKM-type theorems for weakly generalized KKM mapping with some applications
zbMATH Open document ID: 1213.54084
author: Li-Zhi Zhu
author: Jinwang Liu
author: Gu-Sheng Tang
author: Cao-zong Cheng
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2010-04-23T00:00:00Z
review text: The authors introduce the notion of weakly generalized KKM mappings for set--valued mappings \(S:X\to 2^Y,\) where \(X\) is a nonempty set and \(Y\) is a topological space, in order to establish some generalized KKM type theorems without any convexity structure. In Section 3 they present some intersection theorems and generalized KKM type theorems. In particular, in Theorem 3.1, they prove that a weakly generalized KKM mapping with nonempty closed values has the finite intersection property. In Section 4 some minimax inequalities are provided, while in Section 5 the authors present an existence theorem for an abstract generalized vector equilibrium problem.
reviewed by: Rita Pini
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 5700784
zbMATH Keywords: weakly generalized KKM mapping
zbMATH Keywords: generalized KKM--type theorem
zbMATH Keywords: weakly generalized diagonally quasi--convex
zbMATH Keywords: \((W,S,K)\) mapping pair
zbMATH Keywords: generalized vector equilibrium
MaRDI profile type: Publication
full work available at URL: s10255-008-8283-7
OpenAlex ID: W2005260895
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DOI: 10.1007/S10255-008-8283-7
description: scientific article; zbMATH DE number 5700784