Fixed Point Theorem via Measure of Non-Compactness for a New Kind of Contractions.

In this paper, we will use the notion of -admissible mappings in Banach spaces, to introduce the concept of -contractive mappings and establish a fixed point theorem for this type of contractions. Our theorems generalize and improve many results in the literature. Moreover, we apply the main result to prove the existence of a solution for Volterra-integral equation, under more general assumptions than previously made. [ABSTRACT FROM AUTHOR]