a generalization of darbo’s theorem with application to the‎ ‎solvability of systems of integral-differential equations in sobolev spaces

In this article, we introduce the notion of (α, β)-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.