The Distributional Henstock-Kurzweil Integral and Applications: A Survey (Journal of Mathematical Study, 2021)
This study presents a summary of the current state of research on the distributionalHenstock-Kurzweil integral. Basic properties such as integration by parts,Hake theorem, inner product, Hölder inequality, second mean value theorem, orderings,Banach lattice, convergence theorems, fixed point theorems, are shown. Thisstudy also summarizes its applications in integral and differential equations.
Keywords: Distributional Henstock-Kurzweil integral; Banach lattice; convergence theorem; cone; fixed point theorem; integral and differential equations.