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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 147409, 9 pages
http://dx.doi.org/10.1155/2013/147409
Research Article

The Existence and Attractivity of Solutions of an Urysohn Integral Equation on an Unbounded Interval

1Mathematics Department, Science Faculty for Girls, King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland
3Mathematics Depertment, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Received 21 August 2013; Accepted 4 September 2013

Academic Editor: Mohammad Mursaleen

Copyright © 2013 Mohamed Abdalla Darwish 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 a result on the existence and uniform attractivity of solutions of an Urysohn integral equation. Our considerations are conducted in the Banach space consisting of real functions which are bounded and continuous on the nonnegative real half axis. The main tool used in investigations is the technique associated with the measures of noncompactness and a fixed point theorem of Darbo type. An example showing the utility of the obtained results is also included.