Document Type : Research Paper
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, TN, INDIA
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mathematics, Texas A & M University - Kingsville - 78363-8202, Texas, USA
We propose to investigate the solutions of system of functional-integral equations in the setting of measure of noncompactness on real-valued bounded and continuous Banach space. To achieve this, we first establish some new Darbo type fixed and coupled fixed point results for $\mu$-set $(\omega,\vartheta)$-contraction operator using arbitrary measure of noncompactness in Banach spaces. An example is given in support for the solutions of a pair of system of functional-integral equations.