The Existence of Fixed Points via the Measure of Noncompactness and its Application to Functional-Integral Equations

In the present paper, using the concept of measure of non-compactness, we introduce the concept of a new contraction on a Banach space and obtain few generalizations of Darbo’s fixed-point theorem and extend some recent results of (Aghajani et al., J. Comput. Appl. Math. 260:68–77, 2014) and (Aghajani et al., Bull. Belg. Math. Soc. Simon Stevin 20:345–358, 2013). Also we show the applicability of obtained results to the theory of integral equations. A concrete example illustrating the mentioned applicability is also included.