Multivalued fixed point theorems without strong compactness via a generalization of midpoint convexity
type: Item
instance of: scholarly article
zbMATH Open document ID: 1334.47051
author: Irene Benedetti
author: Stella Bolognini
author: Anna Martellotti
publication date: 2014-10-27T00:00:00Z
full work available at URL: http://www.math.ubbcluj.ro/~nodeacj/download.php
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47N10
Mathematics Subject Classification ID: 91A06
zbMATH DE Number: 6361893
zbMATH Keywords: set valued map
zbMATH Keywords: fixed point, convex-valued map
zbMATH Keywords: midpoint linear maps, \(n\)-player game
MaRDI profile type: Publication
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title: Multivalued fixed point theorems without strong compactness via a generalization of midpoint convexity
published in: Fixed Point Theory
review text: The paper introduces the notions of a strongly and weakly midpoint linear multivalued maps, convex and midpoint convex multivalued maps, studies relations between these concepts, sufficient and necessary conditions. Several results concerning the existence of fixed points of such maps are established. As it appears, the structural assumptions (involving the midpoint properties) along with upper-semicontinuity allow to relax the usual compactness conditions. The abstract results are applied to show the existence of equilibria for some specific \(n\)-player games.
reviewed by: Wojciech Kryszewski
description: scientific article; zbMATH DE number 6361893