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A generalization of Darbo's theorem with application to the solvability of systems of integral-differential equations in Sobolev spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 23، دوره 12، شماره 1، مرداد 2021، صفحه 287-300 اصل مقاله (499.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4784 | ||
| نویسندگان | ||
| Hojjatollah Amiri Kayvanloo1؛ Mahnaz Khanehgir1؛ Reza Allahyari* 2 | ||
| 1Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran | ||
| 2Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. | ||
| تاریخ دریافت: 29 تیر 1397، تاریخ بازنگری: 17 شهریور 1398، تاریخ پذیرش: 26 شهریور 1399 | ||
| چکیده | ||
| In this article, we introduce the notion of $(\alpha,\beta)$-generalized Meir-Keeler condensing operator in a Banach space, a characterization using strictly L-functions and provide an extension of Darbo's fixed point theorem associated with measures of noncompactness. Then, we establish some results on the existence of coupled fixed points for a class of condensing operators in Banach spaces. As an application, we study the problem of existence of entire solutions for a general system of nonlinear integral-differential equations in a Sobolev space. Further, an example is presented to verify the effectiveness and applicability of our main results. | ||
| کلیدواژه‌ها | ||
| Coupled fixed points؛ Measure of noncompactness؛ Meir-Keleer condensing operator؛ Sobolev space؛ System of integral equations | ||
| مراجع | ||
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