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On Krasnoselskii's Cone Fixed Point Theorem
Fixed Point Theory and Applications volume 2008, Article number: 164537 (2008)
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.
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Kwong, M.K. On Krasnoselskii's Cone Fixed Point Theorem. Fixed Point Theory Appl 2008, 164537 (2008). https://doi.org/10.1155/2008/164537
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DOI: https://doi.org/10.1155/2008/164537