Some Convergence Theorems of Henstock-Kurzweil-Dunford-Stieltjes Integral and Henstock-Kurzweil- Pettis-Stieltjes Integral of Banach-Valued Functions on \(\mathbb{R}\)
Darwin P. Mangubat *
Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
Greig Bates C. Flores
Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
*Author to whom correspondence should be addressed.
Abstract
Let X be an arbitrary Banach space. The establishment of the Henstock-Kurzweil-Dunford-Stieltjes (HKDS) Integral and Henstock-Kurzweil-Pettis-Stieltjes (HKPS) Integral of an X-valued function over \(\mathbb{R}\) shows a viable and more generalized integration process utilizing the notion of dual spaces and weakly measurable functions. In this manuscript, the authors have discussed about some convergence theorems of Henstock- Kurzweil-Dunford-Stieltjes Integral and Henstock-Kurzweil-Pettis-Stieltjes Integral of X-valued functions on \(\mathbb{R}\) via uniform convergence with respect to the integrand and integrator.
Keywords: HKDS integral, HKPS integral, bounded variation, uniform convergence, 2020