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: In this paper, we establish two fixed point theorems of Krasnoselskii type for the sum of , where is a compact operator and 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

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.