Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE RELATION BETWEEN HENSTOCK INTEGRAL AND HENSTOCK DELTA INTEGRAL ON TIME SCALES

  • Park, Jae Myung (Department of Mathematics Chungnam National University) ;
  • Lee, Deok Ho (Department of Mathematics Education KongJu National University) ;
  • Yoon, Ju Han (Department of Mathematics Education Chungbuk National University) ;
  • Kim, Young Kuk (Department of Mathematics Education Seowon University) ;
  • Lim, Jong Tae (Department of Mathematics Chungnam National University)
  • Received : 2013.06.19
  • Accepted : 2013.07.16
  • Published : 2013.08.15
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Abstract

In this paper, we define an extension $f^*:[a,b]{\rightarrow}\mathbb{R}$ of a function $f^*:[a,b]_{\mathbb{T}}{\rightarrow}\mathbb{R}$ for a time scale $\mathbb{T}$ and show that $f$ is Henstock delta integrable on $[a,b]_{\mathbb{T}}$ if and only if $f^*$ is Henstock integrable on $[a, b]$.

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References

  1. R. Agarwal and M. Bohner, Basic calculus on time scales and some of its applications, Results Math. 35 (1999), 3-22. https://doi.org/10.1007/BF03322019
  2. S. Avsec, B. Bannish, B. Johnson, and S. Meckler, The Henstock-Kurzweil delta integral on unbounded time scales, PanAmerican Math. J. Vol 16 (2006), no. 3, 77-98.
  3. G. Sh. Guseinov, Intergration on time scales, J. Math. Anal. Appl. 285 (2003), 107-127. https://doi.org/10.1016/S0022-247X(03)00361-5
  4. G. Sh. Guseinov and B. Kaymakcalan, Basics of Riemann delta and nabla integration on time scales, J. Difference Equations Appl., 8 (2002), 1001-1027. https://doi.org/10.1080/10236190290015272
  5. J. M. Park, D. H. Lee, J. H. Yoon, and J. T. Lim, The Henstock and Henstock delta Integrals, Chungcheng J. Math. Soc. 26 (2013), no. 2, 291-298.
  6. A. Perterson and B. Thompson, HenstockCKurzweil Delta and Nabla Integral, J. Math. Anal. Appl. 323 (2006), 162-178. https://doi.org/10.1016/j.jmaa.2005.10.025
  7. Charles W. Swartz, Douglas S Kurtz, Theories of Integration: The Integrals of Riemann Lebesgue, Henstock-Kurzweil, and Mcshane, World Scientific, 2004.
  8. B. S. Thomson, Henstock Kurzweil integtals on time scales, PanAmerican Math J. Vol 18 (2008), no. 1, 1-19.

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