The distributional Henstock-Kurzweil integral and applications II

Volume 10, Issue 1, pp 290--298 http://dx.doi.org/10.22436/jnsa.010.01.27

Publication Date: January 27, 2017 Submission Date: October 30, 2016

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Authors

Wei Liu - College of Science, Hohai University, Nanjing 210098, P. R. China. Guoju Ye - College of Science, Hohai University, Nanjing 210098, P. R. China. Dafang Zhao - College of Science, Hohai University, Nanjing 210098, P. R. China.. - School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, P. R. China.

Abstract

In this paper, we study a special Banach lattice \(D_{HK}\), which is induced by the distributional Henstock-Kurzweil integral, and discuss its lattice properties. We show that \(D_{HK}\) is an AM-space with the Archimedean property and the Dunford-Pettis property but it is not Dedekind complete. We also present two fixed point theorems in \(D_{HK}\). Meanwhile, two examples are worked out to demonstrate the results.

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Keywords

• Distributional Henstock-Kurzweil integral
• Banach lattice
• AM-space
• Archimedean property
• Dunford-Pettis property
• order continuity

MSC

•  46B42
•  47H10
•  26A42
•  46G12

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