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.
Amiri Kayvanloo, H., Khanehgir, M., Allahyari, R. (2021). 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, 12(1), 287-300. doi: 10.22075/ijnaa.2021.4784
MLA
Hojjatollah Amiri Kayvanloo; Mahnaz Khanehgir; Reza Allahyari. "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, 12, 1, 2021, 287-300. doi: 10.22075/ijnaa.2021.4784
HARVARD
Amiri Kayvanloo, H., Khanehgir, M., Allahyari, R. (2021). '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, 12(1), pp. 287-300. doi: 10.22075/ijnaa.2021.4784
VANCOUVER
Amiri Kayvanloo, H., Khanehgir, M., Allahyari, R. 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, 2021; 12(1): 287-300. doi: 10.22075/ijnaa.2021.4784
)