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CHARACTERIZING CONVERGENCE CONDITIONS FOR THE Mα-INTEGRAL

  • Received : 2011.04.12
  • Accepted : 2011.08.25
  • Published : 2011.09.30

Abstract

Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.

Keywords

References

  1. R. A. Gordon, The Integrals of Lebegue, Denjoy, Perron, and Henstock, Grad- uate Studies in Math. 4, Amer. Math. Soc. (1994).
  2. J. M. Park, H. W. Ryu and H. K. Lee, The $M_{\alpha}$-integral, J. Chungcheong Math. 23 (2010), no. 1, 99-108.
  3. J.M. Park, D.H. Lee, J.H. Yoon and H.K. Lee, The integration by parts for the $M_{\alpha}$integral, J. Chungcheong Math. 23 (2010), no. 4, 861-870.