Abstract and Applied Analysis
Volume 2013 (2013), Article ID 537897, 15 pages
http://dx.doi.org/10.1155/2013/537897
Research Article

The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations

Józef Banaś1 and Szymon Dudek2

1Department of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 8, 35-959 Rzeszów, Poland
2Department of Mathematics and Natural Sciences, State Higher School of Technology and Economics in Jarosław, Czarnieckiego 16, 37-500 Jarosław, Poland

Received 21 February 2013; Accepted 3 April 2013

Academic Editor: Yisheng Song

Copyright © 2013 Józef Banaś and Szymon Dudek. 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 study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally, that technique allows us to obtain some characterization of considered integral equations. An example illustrating the obtained results is also included.