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http://dx.doi.org/10.14403/jcms.2015.28.1.53

THE RIEMANN-STIELTJES DIAMOND-ALPHA INTEGRAL ON TIME SCALES  

Zhao, Dafang (School of Mathematics and Statistics Hubei Normal University)
You, Xuexiao (School of Mathematics and Statistics Hubei Normal University)
Cheng, Jian (School of Mathematics and Statistics Hubei Normal University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.28, no.1, 2015 , pp. 53-63 More about this Journal
Abstract
In this paper, we define and study the Riemann-Stieltjes diamond-alpha integral on time scales. Many properties of this integral will be obtained. The Riemann-Stieltjes diamond-alpha integral contains the Riemann{Stieltjes integral and diamond-alpha integral as special cases.
Keywords
time scales; diamond-alpha integral; Riemann-Stieltjes integral;
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1 S. Hilger, Ein Makettenkalkl mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph. D. Thesis, Universtat Wurzburg, 1988.
2 S. Hilger, Analysis on measure chains- A unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18-56.   DOI
3 M. Bohner, A. Peterson, Dynamic equations on time scales. An introduction with applications, BirkhauserBoston, Boston, MA, 2001.
4 M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2004.
5 M. Bohner and G. S. Guseinov, The convolution on time scales, Abstr. Appl. Anal. Vol. 2007, Article ID 58373, 24 pages.
6 A. Peterson and B. Thompson, Henstock-Kurzweil Delta and Nabla Integrals,, J. Math. Anal. Appl. 323 (2006), 162-178.   DOI   ScienceOn
7 B. Thompson, Henstock-Kurzweil integrals on time scales, Panamer. Math. J. 18 (2008), no. 1, 1-19.
8 D. Mozyrska, E. Paw luszewicz, and D. F. M. Torres, The Riemann-Stieltjes intergral on time scales, Aust. J. Math. Anal. Appl. 7 (2010), no. 1, 1-14.
9 J. W. Rogers and Jr., Q. Sheng, Notes on the diamond-${\alpha}$ dynamic derivative on time scales, J. Math. Anal. Appl. 326 (2007), no. 1, 228-241.   DOI   ScienceOn
10 Q. Sheng, M. Fadag, J. Henderson, and J. M. Davis, An exploration of combined dynamic derivatives on time scales and their applications, Nonlinear Anal. Real World Appl. 7 (2006), no. 3, 395-413.   DOI   ScienceOn
11 D. Mozyrska and D. F. M. Torres, A Study of Diamond-alpha dynamic equations on regular time scales, Afr. Diaspora J. Math. 8 (2009), no. 1, 35-47.
12 A. B. Malinowska and D. F. M. Torres, The diamond-alpha Riemann integral and mean value theorems on time scales, Dynamic Systems and Applications 18 (2009), 469-482.