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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Krasnoselskii type fixed point theorems and applications


Authors: Yicheng Liu and Zhixiang Li
Journal: Proc. Amer. Math. Soc. 136 (2008), 1213-1220
MSC (2000): Primary 47H10, 34K13
Published electronically: December 5, 2007
MathSciNet review: 2367095
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we establish two fixed point theorems of Krasnoselskii type for the sum of $ A+B$, where $ A$ is a compact operator and $ I-B$ may not be injective. Our results extend previous ones. As an application, we apply such results to obtain some existence results of periodic solutions for delay integral equations and then give three instructive examples.


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Additional Information

Yicheng Liu
Affiliation: Department of Mathematics and System Science, College of Science, National University of Defense Technology, Changsha, 410073, People’s Republic of China.
Email: liuyc2001@hotmail.com

Zhixiang Li
Affiliation: Department of Mathematics and System Science, College of Science, National University of Defense Technology, Changsha, 410073, People’s Republic of China.
Email: zhxli02@yahoo.com.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09190-3
PII: S 0002-9939(07)09190-3
Keywords: Fixed point theorem, separate contraction mapping, periodic solution, multi-valued mapping, delay integral equation.
Received by editor(s): July 28, 2004
Received by editor(s) in revised form: December 20, 2005
Published electronically: December 5, 2007
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.