The distributional Henstock–Kurzweil integral and applications

Abstract

In this paper, we study the distributional Henstock–Kurzweil integral and its properties, such as strong and weak convergence theorems. We also establish the structure of the space of Henstock–Kurzweil integrable distributions, which is proved to be an ordered Banach space with a regular cone. Furthermore, fixed point theorems in such space are presented to deal with nonlinear integral equations involving this integral.