Mathematical Researches

In this paper, using the concept of measure of noncompactness, we introduce a new extended contraction of operators on a Banach space and obtain some generalizations of Darbo’s fixed-point theorem. In the following, as an application of the obtained results, we deal with the solvability of a system of integral equations of Stochastic type in Banach space. Our results generalize and extend a lot of comparable results in the literature. Finally, a concrete example is also included, which demonstrates the applicability of the obtained results.