On Krasnoselskii's Cone Fixed Point Theorem

<p<Abstract</p< <p<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 p...
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Autor*in:	Kwong ManKam [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2008

Übergeordnetes Werk:	In: Fixed Point Theory and Applications - SpringerOpen, 2006, (2008), 1, p 164537
Übergeordnetes Werk:	year:2008 ; number:1, p 164537

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Katalog-ID:	DOAJ061670707

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allfieldsSound	(DE-627)DOAJ061670707 (DE-599)DOAJ5cabcb2f826f4afb818b1c94417b3643 DE-627 ger DE-627 rakwb eng T57-57.97 QA299.6-433 Kwong ManKam verfasserin aut On Krasnoselskii's Cone Fixed Point Theorem 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier <p<Abstract</p< <p<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.</p< Applied mathematics. Quantitative methods Analysis In Fixed Point Theory and Applications SpringerOpen, 2006 (2008), 1, p 164537 (DE-627)379482037 (DE-600)2135860-6 16871812 nnns year:2008 number:1, p 164537 https://doaj.org/article/5cabcb2f826f4afb818b1c94417b3643 kostenfrei http://www.fixedpointtheoryandapplications.com/content/2008/164537 kostenfrei https://doaj.org/toc/1687-1820 Journal toc kostenfrei https://doaj.org/toc/1687-1812 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2008 1, p 164537
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author	Kwong ManKam
spellingShingle	Kwong ManKam misc T57-57.97 misc QA299.6-433 misc Applied mathematics. Quantitative methods misc Analysis On Krasnoselskii's Cone Fixed Point Theorem
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topic_title	T57-57.97 QA299.6-433 On Krasnoselskii's Cone Fixed Point Theorem
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title	On Krasnoselskii's Cone Fixed Point Theorem
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title_sort	on krasnoselskii's cone fixed point theorem
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title_auth	On Krasnoselskii's Cone Fixed Point Theorem
abstract	<p<Abstract</p< <p<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.</p<
abstractGer	<p<Abstract</p< <p<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.</p<
abstract_unstemmed	<p<Abstract</p< <p<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.</p<
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