  The objective of this manuscript is to enquire for the solvability of a
specific type of non-linear quadratic integral equations via the interesting
notion of measure of non-compactness. Firstly, we inquire into couple of
exciting fixed point theorems involving a measure of non-compactness in the
setting of a Banach space. Subsequently, bringing into play a suitable measure
of non-compactness and the acquired results, we discuss the existence of
solution to the aforementioned kind of non-linear quadratic integral equations.
