Fixed point theorems for decreasing operators in ordered Banach spaces with lattice structure and their applications
type: Item
instance of: scholarly article
title: Fixed point theorems for decreasing operators in ordered Banach spaces with lattice structure and their applications
zbMATH Open document ID: 1295.47059
DOI: 10.1186/1687-1812-2013-18
author: Xingchang Li
author: Zhihao Wang
published in: Fixed Point Theory and Applications
publication date: 2014-01-29T00:00:00Z
review text: Let \(E\) be an ordered Banach space with lattice structure. The following are the main results of the authors: {Theorem 1.} Suppose that \(D\subseteq E\) is bounded and \(A:D\to D\) is a decreasing condensing operator. Then \(A\) has a fixed point in \(D\). {Theorem 2.} Suppose that \(P\subseteq E\) is a normal cone and \(A:E\to E\) is a decreasing condensing operator. Then \(A\) has a fixed point in \(E\). An application of these results to uniformly elliptic differential problems is given.
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 47H08
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 6251570
zbMATH Keywords: Banach space with lattice structure
zbMATH Keywords: condensing operator
zbMATH Keywords: decreasing operator
zbMATH Keywords: fixed point
zbMATH Keywords: elliptic equation
Wikidata QID: Q59301888
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1186/1687-1812-2013-18
OpenAlex ID: W2114114687
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description: scientific article; zbMATH DE number 6251570