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

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Abstract

In this paper, we introduce a (Henstock–Kurzweil) HK-type integral with respect to a \(\theta \) 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 \(SH_1\) integral, can be characterized using this HK-type integral. Also, we introduce the concepts of \(AC^*\) and \(ACG^*\) along with other important concepts, and define a Denjoy-type integral. This integral is shown to be equivalent to the \(SH_1\) integral.

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Authors and Affiliations

  1. Mathematics Department, Mapua University, Manila City, 1002, Philippines

    Rodolfo Maza & Sergio R. Canoy Jr.

  2. Center for Mathematical and Theoretical Physical Sciences-PRISM, Mindanao State University - Iligan Institute of Technology, Iligan City, 9200, Philippines

    Sergio R. Canoy Jr.

Authors
  1. Rodolfo Maza
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  2. Sergio R. Canoy Jr.
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Correspondence to Rodolfo Maza.

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Maza, R., Canoy, S.R. A Denjoy-type integral and a strongly henstock integral in locally convex topological vector space. Rend. Circ. Mat. Palermo, II. Ser 73, 1677–1700 (2024). https://doi.org/10.1007/s12215-024-01008-4

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  • DOI: https://doi.org/10.1007/s12215-024-01008-4

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