A Denjoy-type integral and a strongly henstock integral in locally convex topological vector space

In this paper, we introduce a (Henstock–Kurzweil) HK-type integral with respect to a \(\theta \) $\theta$ neighborhood using the Minkowski functional in a locally convex topological vector space (LCTVS). It is shown that a strongly HK integral, also called here the \(SH_1\) $S{H}_1$ integral, can be characterized using this HK-type integral. Also, we introduce the concepts of \(AC^*\) $A{C}^{\ast }$ and \(ACG^*\) $AC{G}^{\ast }$ along with other important concepts, and define a Denjoy-type integral. This integral is shown to be equivalent to the \(SH_1\) $S{H}_1$ integral.