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Volume 49, Issue 4
The Distributional Henstock-Kurzweil Integral and Applications: A Survey

Guoju Ye & Wei Liu

DOI: 10.4208/jms.v49n4.16.06

J. Math. Study, 49 (2016), pp. 433-448.

Published online: 2016-12

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  • Abstract

This study presents a summary of the current state of research on the distributional Henstock-Kurzweil integral. Basic properties such as integration by parts, Hake theorem, inner product, Hölder inequality, second mean value theorem, orderings, Banach lattice, convergence theorems, fixed point theorems, are shown. This study also summarizes its applications in integral and differential equations.

  • Keywords

Distributional Henstock-Kurzweil integral, Banach lattice, convergence theorem, cone, fixed point theorem, integral and differential equations.

  • AMS Subject Headings

45G10, 26A42, 46F30, 46F05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yegj@hhu.edu.cn (Guoju Ye)

liuw626@hhu.edu.cn (Wei Liu)

  • BibTex
  • RIS
  • TXT
@Article{JMS-49-433, author = {Ye , Guoju and Liu , Wei}, title = {The Distributional Henstock-Kurzweil Integral and Applications: A Survey}, journal = {Journal of Mathematical Study}, year = {2016}, volume = {49}, number = {4}, pages = {433--448}, abstract = {

This study presents a summary of the current state of research on the distributional Henstock-Kurzweil integral. Basic properties such as integration by parts, Hake theorem, inner product, Hölder inequality, second mean value theorem, orderings, Banach lattice, convergence theorems, fixed point theorems, are shown. This study also summarizes its applications in integral and differential equations.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n4.16.06}, url = {http://global-sci.org/intro/article_detail/jms/10121.html} }
TY - JOUR T1 - The Distributional Henstock-Kurzweil Integral and Applications: A Survey AU - Ye , Guoju AU - Liu , Wei JO - Journal of Mathematical Study VL - 4 SP - 433 EP - 448 PY - 2016 DA - 2016/12 SN - 49 DO - http://doi.org/10.4208/jms.v49n4.16.06 UR - https://global-sci.org/intro/article_detail/jms/10121.html KW - Distributional Henstock-Kurzweil integral, Banach lattice, convergence theorem, cone, fixed point theorem, integral and differential equations. AB -

This study presents a summary of the current state of research on the distributional Henstock-Kurzweil integral. Basic properties such as integration by parts, Hake theorem, inner product, Hölder inequality, second mean value theorem, orderings, Banach lattice, convergence theorems, fixed point theorems, are shown. This study also summarizes its applications in integral and differential equations.

Guoju Ye & Wei Liu. (2019). The Distributional Henstock-Kurzweil Integral and Applications: A Survey. Journal of Mathematical Study. 49 (4). 433-448. doi:10.4208/jms.v49n4.16.06
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