On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales

Volume 10, Issue 5, pp 2487--2500 http://dx.doi.org/10.22436/jnsa.010.05.18

Publication Date: May 25, 2017 Submission Date: January 17, 2017

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Authors

Xuexiao You - School of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, P. R. China. - College of Computer and Information, Hohai University, Nanjing, Jiangsu 210098, P. R. China. Dafang Zhao - School of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, P. R. China. - College of Science, Hohai University, Nanjing, Jiangsu 210098, P. R. China. Delfim F. M. Torres - Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal.

Abstract

We introduce and investigate the Henstock-Kurzweil (HK) integral for Riesz-space-valued functions on time scales. Some basic properties of the HK delta integral for Riesz-space-valued functions are proved. Further, we prove uniform and monotone convergence theorems.

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Keywords

• Henstock-Kurzweil integral
• Riesz space
• time scales.

MSC

•  28B05
•  28B10
•  28B15
•  46G10

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