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

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 K. Maleknejad , K. Nouri , and R. Mollapourasl ( 2009 ). Investigation on the existence of solutions for some nonlinear functional-integral equations . Nonlinear Anal. 71 : 1575 – 1578 .[Crossref], [Web of Science ®] , [Google Scholar]] and Özdemir et al. [8 ?. Özdemir , Ü. Çakan , and B. ?lhan ( 2013 ). On the existence of the solutions for some nonlinear Volterra integral equations . Abstr. Appl. Anal. Article ID 689234.  [Google Scholar]] as special cases under some weaker conditions. We give also some examples which show that our results are applicable.