Year: 2025
Type: article
Abstract: We introduce Henstock-Kurzweil integrability for functions whose values lies in the quotient space on time scales. We define the Henstock-Kurzweil integral with respect to the Δ-derivative and ∇-derivative namely the quotient Henstock-Kurzweil Δ-integral and quotient Henstock-Kurzweil ∇-integral respectively. Result establishing the criterion of integrability is observed, and few properties of the integrals are formulated.Relations between quotient Henstock-Kurzweil integral and quotient Riemann integral, and quotient Henstock-Kurzweil integral and Banach Henstock-Kurzweil integral are also presented. In addition, as a linear combination of the Δ- and ∇-integrals we introduce the quotient Henstock-Kurzweil ♢α-integral and conclude with a theorem depicting the relation between the three integrals.
DOI: 10.5269/bspm.77567
Authors: Vikuozonuo Sekhose, Hemen Bharali
Institution: Assam Don Bosco University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7083311773