Journal of the
Korean Mathematical Society JKMS

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banach space via the measure of non-compactness, which generalize the result of Aghajani et al.~\cite{ag4}. Our results generalize, extend, and unify several well-known comparable results in the literature. One of the applications of our main result is to prove the existence of solutions for the system of integral equations.

Keywords: measure of noncompactness, fixed point, coupled fixed point, system of integral equations

MSC numbers: 47H09, 47H10