Some Fundamental Properties of Variational Kurzweil-Henstock-Stieltjes Integral on a Compact Interval in Rn
Develin O. Omayan *
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
Greig Bates C. Flores
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
*Author to whom correspondence should be addressed.
Abstract
Hoffman introduced the variational Kurzweil-Hentock-Stieltjes integral on a real-valued function and presented some of its properties. In this paper, we defined the variational Kurzweil-Henstock-Stieltjes integral on a compact interval in Rn. Fundamental properties such as uniqueness, linearity property and monotonocity property of both the integrand and integrator, additivity and integrability over a subinterval are provided. In addition, a characterization of the variational Kurzweil-Henstock-Stieltjes integral is established by formulating the Cauchy Criterion.
Keywords: Variational kurzweil-henstock-stieltjes integral, PUL-stieltjes integral