Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6570
Title: On Krasnoselskii's cone fixed point theorem
Authors: Kwong, MK
Keywords: Fixed point arithmetic
Nonlinear equations
Topology
Issue Date: 17-Mar-2008
Publisher: Springer
Source: Fixed point theory and applications, 17 Mar. 2008, v. 2008, 164537, p. 1-18 How to cite?
Journal: Fixed point theory and applications 
Abstract: In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
URI: http://hdl.handle.net/10397/6570
ISSN: 1687-1820
EISSN: 1687-1812
DOI: 10.1155/2008/164537
Rights: Copyright © 2008 Man Kam Kwong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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