An Application of Darbo Fixed-Point Theorem to a Class of Functional Integral Equations |
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Authors: | Ümit Çakan İsmet Özdemir |
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Affiliation: | 1. Fen Edebiyat Fakültesi, Matematik B?lümü , Nev?ehir Hac? Bekta? Veli üniversitesi , Nev?ehir , Turkey umitcakan@nevsehir.edu.tr;3. E?itim Fakültesi , ?n?nü üniversitesi , Malatya , Turkey |
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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 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. |
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Keywords: | Darbo fixed-point theorem Measure of noncompactness Nonlinear integral equations |
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