Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24079
Title: The topological nature of Krasnoselskii's cone fixed point theorem
Authors: Kwong, MK
Keywords: Cone fixed point theorem
Krasnoselskii
Issue Date: 2008
Publisher: Pergamon Press
Source: Nonlinear analysis : theory, methods and applications, 2008, v. 69, no. 3, p. 891-897 How to cite?
Journal: Nonlinear analysis : theory, methods 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 this article we discuss the topological nature of the Krasnoselskii theorem and show that it can be restated in a more general form without reference to a cone structure or the norm of the underlying Banach space. This new perspective brings out a closer relation between the Krasnoselskii Theorem and the classical Brouwer fixed point theorem. It also points to some obvious extensions of the cone theorem.
URI: http://hdl.handle.net/10397/24079
ISSN: 0362-546X
DOI: 10.1016/j.na.2008.02.060
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