Some Convergence Theorems of Henstock-Kurzweil-Dunford-Stieltjes Integral and Henstock-Kurzweil- Pettis-Stieltjes Integral of Banach-Valued Functions on \(\mathbb{R}\)

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.