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The distributional Henstock–Kurzweil integral and applications

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Abstract

In this paper, we study the distributional Henstock–Kurzweil integral and its properties, such as strong and weak convergence theorems. We also establish the structure of the space of Henstock–Kurzweil integrable distributions, which is proved to be an ordered Banach space with a regular cone. Furthermore, fixed point theorems in such space are presented to deal with nonlinear integral equations involving this integral.

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Acknowledgments

The authors are grateful to the referee for the careful reading and helpful comments.

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Authors and Affiliations

  1. College of Sciences, Hohai University, Nanjing, 210098, People’s Republic of China

    Guoju Ye & Wei Liu

Authors
  1. Guoju Ye
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  2. Wei Liu
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Corresponding author

Correspondence to Wei Liu.

Additional information

Communicated by G. Teschl.

Supported by the Fundamental Research Funds for the Central Universities (No. 2014B38114).

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Ye, G., Liu, W. The distributional Henstock–Kurzweil integral and applications. Monatsh Math 181, 975–989 (2016). https://doi.org/10.1007/s00605-015-0853-1

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  • DOI: https://doi.org/10.1007/s00605-015-0853-1

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