Quotient space Henstock-Kurzweil integration on time scales

Vikuozonuo   Sekhose; Hemen Bharali

doi:10.5269/bspm.77567

Vikuozonuo Sekhose Assam Don Bosco University, India https://orcid.org/0009-0007-1465-1604
Hemen Bharali Assam Don Bosco University https://orcid.org/0000-0002-4800-9536

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.

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