Abstract convexity in KKM theorems via set-valued maps
type: Item
instance of: scholarly article
title: Abstract convexity in KKM theorems via set-valued maps
zbMATH Open document ID: 1478.47041
published in: Optimization Letters
publication date: 2021-05-05T00:00:00Z
review text: \textit{B. Knaster} et al. [Fundam. Math. 14, 132--137 (1929; JFM 55.0972.01)] proved the well-known KKM lemma which is an equivalent form of the Brouwer fixed point theorem. Some researchers tried to present the KKM results such as generalized L-KKM type theorems in the absence of usual convexity. In this paper, the authors present a counterexample to show that the main results in some generalized KKM type theorems and their consequence are not valid. Then, by using upper semicontinuous set-valued maps, the authors introduce the concept of uniform map convex space and prove a nonempty intersection result in this space.
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 58C06
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 7343989
zbMATH Keywords: KKM lemma
zbMATH Keywords: uniform map convex space
zbMATH Keywords: \(\Phi\)-KKM map
author: M. Fakhar
author: Maryam Lotfipour
author: Jafar Zafarani
reviewed by: I. M. Stancu-Minasian
MaRDI profile type: Publication
full work available at URL: s11590-020-01536-9
OpenAlex ID: W3002548451
Wikidata QID: Q126299772
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DOI: 10.1007/S11590-020-01536-9
description: scientific article; zbMATH DE number 7343989