We propose two new notion of contraction mappings involving measure of noncompactness in the frame work of Banach space and derive some basic Darbo type fixed and coupled fixed point results. The results are correlated with the classical Banach fixed point theorems. Further we show the applicability of obtained results to the theory of integral equations following a concrete example which illustrate the application part. © 2017, Akadémiai Kiadó, Budapest, Hungary.