On statistical convergence of topological q-Henstock-Kurzweil integral

Abstract

In this paper, we present the concept of an q-Henstock-Kurzweil-type integrable function (here-after referred to as a q-topological Henstock-Kurzweil integrable function) within a topological vector space linked to a Radon measure μ. Fundamental findings concerning the topological Henstock-Kurzweil integrable function are examined. Furthermore, the connection between the topological q-Henstock-Kurzweil integral and the topological Henstock-Kurzweil integral is analyzed. Finally, we extend the concept of statistical convergence to topological q-Henstock-Kurzweil integrable functions within a μ-subcell of a topological vector space.