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Journal of Function Spaces
Volume 2014, Article ID 324082, 9 pages
Research Article

Existence and Asymptotic Stability of Solutions of a Functional Integral Equation via a Consequence of Sadovskii’s Theorem

1Department of Mathematics, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland
2Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Faculty of Science, Damanhour University, Damanhour 22511, Egypt
4Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus deTafira Baja, 35017 Las Palmas de Gran Canaria, Spain

Received 3 May 2014; Accepted 12 June 2014; Published 16 July 2014

Academic Editor: Józef Banaś

Copyright © 2014 Agnieszka Chlebowicz 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.


Using the technique of measures of noncompactness and, in particular, a consequence of Sadovskii’s fixed point theorem, we prove a theorem about the existence and asymptotic stability of solutions of a functional integral equation. Moreover, in order to illustrate our results, we include one example and compare our results with those obtained in other papers appearing in the literature.