On μF-contraction: New types of fixed points and common fixed points in Banach spaces

Abstract

In this work, we define a new notion of [Formula: see text]-contraction in Banach spaces, by modeling with measure of non-compactness the well-known concept of [Formula: see text]-contraction given by Wardowski in metric spaces. We prove a fixed-point theorem and a common fixed-point theorem for our contraction. Our results extend the well-known Darbo contraction principle and large contractions in the literature. Furthermore, the paper contains examples and applications that show the validity of our results.