The fixed point property in \(c_{0}\) with the alpha norm
type: Item
instance of: scholarly article
zbMATH Open document ID: 1316.46016
author: Berta Gamboa de Buen
author: Fernando Núñez-Medina
publication date: 2014-10-27T00:00:00Z
full work available at URL: http://www.math.ubbcluj.ro/~nodeacj/download.php
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 6361925
zbMATH Keywords: fixed point property
zbMATH Keywords: space \(c_{0\alpha}\)
MaRDI profile type: Publication
title: The fixed point property in \(c_{0}\) with the alpha norm
published in: Fixed Point Theory
review text: The authors prove the followingNEWLINENEWLINE Theorem 2.2. Let \(K\) be a nonempty closed convex and bounded subset of \(c_{0\alpha}= (c_0,\|\cdot\|_\alpha)\), where NEWLINE\[NEWLINE\| (x_i)\|_\alpha= \sup_i|x_i|+\alpha \sum_i{|x_i|\over 2^i},\quad \alpha\geq 0.NEWLINE\]NEWLINE Then \(K\) is weakly compact if and only if every nonempty closed convex subset \(M\subset K\) has the FPP (i.e., for every non-expansive mapping \(T: M\to M\) we have \(\text{Fix}(T)\neq\emptyset\)).
reviewed by: Jarosław Górnicki
description: scientific article; zbMATH DE number 6361925