DOI QR코드

DOI QR Code

THE HESTOCK AND HENSTOCK DELTA INTEGRALS

  • 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 : 2013.03.18
  • Accepted : 2013.04.18
  • Published : 2013.05.15

Abstract

In this paper, we study the Henstock delta integral, which generalizes the Henstock integral. In particular, we study the relation between the Henstock and Henstock delta integrals.

Keywords

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. A. Perterson and B. Thompson, Henstock CKurzweil Delta and Nabla Integral, J. Math. Anal. Appl. 323 (2006), 162-178. https://doi.org/10.1016/j.jmaa.2005.10.025
  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. Difffference Equations Appl. 8 (2002), 1001-1027. https://doi.org/10.1080/10236190290015272
  5. S. Avsec, B. Bannish, B. Johnson, and S. Meckler, The Henstock-Kurzweil delta integral on unbounded time scales, PanAmerican Math. J. 16 (2006), no. 3, 77-98.
  6. B. S. Thomson, Henstock Kurzweil integtals on time scales, PanAmerican Math J. 18 (2008), no. 1, 1-19.
  7. C. W. Swartz and D. S. Kurtz, Theories of Integration: The Integrals of Riemann Lebesgue, Henstock-Kurzweil, and Mcshane, World Scientific, 2004.