Differential and integral equations with Henstock–Kurzweil integrable functions

Abstract

In this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing Henstock-Kurzweil integrable functions.

Closure properties for integral problems driven by regulated functions via convergence results

“…The Kurzweil-type integrals have been extensively used in many papers on differential or integral equations (such as, in [32] or [38], see also [10], [13], [14], [19] or [29]).…”

On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales

“…It has been shown that the Henstock-Kurzweil integral is equivalent to the Denjoy-Perron integral. For fundamental results and some applications in the theory of Henstock-Kurzweil integration, we refer the reader to the papers [21,22,23,25,30,31,32,61,62,64,66] and monographs [2,28,33,34,36,38,39,40,41,42,43,48,56,57].…”