%0 Journal Article
%T A generalization of Darbo's theorem with application to the solvability of systems of integral-differential equations in Sobolev spaces
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Amiri Kayvanloo, Hojjatollah
%A Khanehgir, Mahnaz
%A Allahyari, Reza
%D 2021
%\ 02/01/2021
%V 12
%N 1
%P 287-300
%! A generalization of Darbo's theorem with application to the solvability of systems of integral-differential equations in Sobolev spaces
%K Coupled fixed points
%K Measure of noncompactness
%K Meir-Keleer condensing operator
%K Sobolev space
%K System of integral equations
%R 10.22075/ijnaa.2021.4784
%X 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.
%U https://ijnaa.semnan.ac.ir/article_4784_690b0b82e08a2f61e248755fad00d3bc.pdf