Abstract
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.
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