Abstract and Applied Analysis
Volume 2012 (2012), Article ID 267531, 23 pages
http://dx.doi.org/10.1155/2012/267531
Research Article

Krasnosel’skii Type Fixed Point Theorems for Mappings on Nonconvex Sets

Maryam A. Alghamdi,1 Donal O'Regan,2 and Naseer Shahzad3

1Department of Mathematics, Faculty of Science for Girls, King Abdulaziz University, P.O. Box 4087, Jeddah 21491, Saudi Arabia
2Department of Mathematics, School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
3Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21859, Saudi Arabia

Received 17 May 2012; Revised 28 August 2012; Accepted 29 August 2012

Academic Editor: Paul Eloe

Copyright © 2012 Maryam A. Alghamdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove Krasnosel'skii type fixed point theorems in situations where the domain is not necessarily convex. As an application, the existence of solutions for perturbed integral equation is considered in p-normed spaces.