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

Abstract

We introduce and investigate the Henstock-Kurzweil (HK) integral for Riesz-space-valued functions on time scales. Some basic properties of the HK delta integral for Riesz-space-valued functions are proved. Further, we prove uniform and monotone convergence theorems.

The Fuzzy Henstock–Kurzweil Delta Integral on Time Scales

“…In [32], Peterson and Thompson introduced a more general concept of integral, i.e., the HK ∆ -integral, which gives a common generalization of the Riemann ∆ and Lebesgue ∆ -integral. The theory of HK integration for real-valued and vectorvalued functions on time scales has been developed rather intensively, see, e.g., the papers [1,11,16,28,29,33,37,40,44] and references cited therein.…”

Some inequalities for interval-valued functions on time scales

“…The aim is to unify various definitions and results from the theories of discrete and continuous dynamical systems, and to extend them to more general classes of dynamical systems. It has undergone tremendous expansion and development on various aspects by several authors over the past three decades: see, e.g., [3,4,5,6,18,19,35,37,39,40,41].…”