Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

Babak Mohammadi, Ali Asghar Shole Haghighi, Maryam Khorshidi, Manuel De la Sen and Vahid Parvaneh
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Babak Mohammadi: Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran
Ali Asghar Shole Haghighi: Department of Mathematics, Payame Noor University, Tehran, Iran
Maryam Khorshidi: Department of Mathematics, Firouzabad Institute of Higher Education, Firouzabad, Fars, Iran
Manuel De la Sen: Institute of Research and Development of Processes University of the Basque Country, 48940 Leioa, Spain
Vahid Parvaneh: Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran

Mathematics, 2020, vol. 8, issue 4, 1-11

Abstract: In this paper, an extension of Darbo’s fixed point theorem via θ - F -contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

Keywords: fixed point; measure of noncompactness; coupled fixed point; integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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