Monotone convergence theorems for Henstock–Kurzweil integrable functions and applications

Abstract

In this paper we prove monotone convergence theorems for Henstock-Kurzweil integrable functions from a compact real interval to an ordered Banach space. These theorems are then applied to prove existence results for solutions of a discontinuous functional integral equation containing Henstock-Kurzweil integrable functions.

Differential and integral equations with Henstock–Kurzweil integrable functions

“…In [8] existence results are derived for the smallest and greatest solutions of a discontinuous functional Urysohn integral equation in ordered Banach spaces containing HK integrable functions. Discontinuous functional differential and integral equations in ordered Banach spaces containing HL integrable or Bochner integrable functions are studied, e.g., in [2, Sections 6 and 7] (see also references therein).…”