An Application of Darbo Fixed-Point Theorem to a Class of Functional Integral Equations

Abstract

In this article, using Darbo's fixed-point theorem associated with the measure of noncompactness, we prove a theorem on the existence of the solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. Our existence results include several existence results obtained earlier by Maleknejad et al. [7] and Özdemir et al. [8] as special cases under some weaker conditions. We give also some examples which show that our results are applicable.

Keywords:

• Darbo fixed-point theorem
• Measure of noncompactness
• Nonlinear integral equations

Mathematics Subject Classification:

• 45M99
• 47H09

ACKNOWLEDGMENTS

The authors would like to thank Professor M. Zuhair Nashed (Editor in Chief) and the referees for their helpful comments and suggestions on the improvement of this article.