Fixed points for set-valued maps: A topological perspective
type: Item
instance of: scholarly article
zbMATH Open document ID: 0997.47043
author: Hichem Ben-El-Mechaiekh
publication date: 2002-07-28T00:00:00Z
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 52A27
zbMATH DE Number: 1667856
zbMATH Keywords: fixed ponts
zbMATH Keywords: space approximation
zbMATH Keywords: admissibility of Klee
zbMATH Keywords: topological notions of convexity
zbMATH Keywords: approximative neighborhood extension spaces
zbMATH Keywords: fixed point principle
zbMATH Keywords: set-valued maps
zbMATH Keywords: Kakutani-Fan-Himmelberg fixed point theorem
MaRDI profile type: Publication
title: Fixed points for set-valued maps: A topological perspective
review text: In this paper a purely topological notion of space approximation, which contains the admissibility of Klee and accommodates recent topological notions of convexity, is defined. The large class of approximative neighborhood extension spaces are shown to have this approximation property. Then he derives a key fixed point principle for set-valued maps which not only allows the passage from basic domains to more elaborate ones but also permits the shifting of compactness from domains to maps. NEWLINENEWLINENEWLINEThe results unify a number of recent generalizations of the Kakutani-Fan-Himmelberg fixed point theorem and shed some light on the role of topology in fixed point theory for set-valued maps.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00060].
reviewed by: Sotiris K. Ntouyas
description: scientific article; zbMATH DE number 1667856