Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON AP-$GR_{k}$ INTEGRAL

  • Yoon, Ju Han (Department of Mathematics Education Chungbuk National University) ;
  • Park, Jae Myung (Department of Mathematics Chungnam University) ;
  • Lee, Deok Ho (Department of Mathematics Education Kongju National University)
  • Published : 2012.02.15
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Abstract

In this paper we define the AP-$GR_{k}$ integral and investigate some properties of this integral. Also, a convergence theorem is proved using equi-integrability conditions.

Keywords

References

  1. P. Y. Lee, Lanzhou Lectures in Henstock Integral, World Scientific, 1989.
  2. S. Pal, D. K. Ganguly and Lee Peng Yee, Henstock-Stieltjes Integrals not induced by measure, Real Analysis Exchange 26 (2000/2001), no. 2, 853-860.
  3. S. Pal, D. K. Ganguly and Lee Peng Yee, The Fundamental Theorem of Calculus for $GR_{k}$ -type Integrals, Real Analysis Exchange 28 (2002/2003), no. 2, 549-562. https://doi.org/10.14321/realanalexch.28.2.0549
  4. J. H. Yoon, J. M. Park, Y. K. Kim, and B. M. Kim, The AP-Henstock Extension of the Dunford and Pettis Integrals. Journal of the Chungcheoug Math. Soc. 23 (2010), no. 4, 799-844.