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The s-Perron, sap-Perron and ap-McShane Integrals

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Abstract

In this paper, we study the s-Perron, sap-Perron and ap-McShane integrals. In particular, we show that the s-Perron integral is equivalent to the McShane integral and that the sap-Perron integral is equivalent to the ap-McShane integral.

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References

  1. P. S. Bullen: The Burkill approximately continuous integral. J. Austral. Math. Soc. Ser. A 35 (1983), 236-253).

    Google Scholar 

  2. T. S. Chew, and K. Liao: The descriptive definitions and properties of the AP-integral and their application to the problem of controlled convergence. Real Analysis Exchange 19 (1993-1994), 81-97.

    Google Scholar 

  3. R. A. Gordon: Some comments on the McShane and Henstock integrals. Real Analysis Exchange 23 (1997-1998), 329-342.

    Google Scholar 

  4. R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Amer. Math. Soc., Providence, 1994.

  5. J. Kurzweil: On multiplication of Perron integrable functions. Czechoslovak Math. J. 23(98) (1973), 542-566.

    Google Scholar 

  6. J. Kurzweil, and J. Jarník: Perron type integration on n-dimensional intervals as an extension of integration of step functions by strong equiconvergence. Czechoslovak Math. J. 46(121) (1996), 1-20.

    Google Scholar 

  7. T. Y. Lee: On a generalized dominated convergence theorem for the AP integral. Real Analysis Exchange 20 (1994-1995), 77-88.

    Google Scholar 

  8. K. Liao: On the descriptive definition of the Burkill approximately continuous integral. Real Analysis Exchange 18 (1992-1993), 253-260.

    Google Scholar 

  9. Y. J. Lin: On the equivalence of four convergence theorems for the AP-integral. Real Analysis Exchange 19 (1993-1994), 155-164.

    Google Scholar 

  10. J. M. Park: Bounded convergence theorem and integral operator for operator valued measures. Czechoslovak Math. J. 47(122) (1997), 425-430.

    Google Scholar 

  11. J. M. Park: The Denjoy extension of the Riemann and McShane integrals. Czechoslovak Math. J. 50(125) (2000), 615-625.

    Google Scholar 

  12. A. M. Russell: Stieltjes type integrals. J. Austral. Math. Soc. Ser. A 20 (1975), 431-448.

    Google Scholar 

  13. A. M. Russell: A Banach space of functions of generalized variation. Bull. Austral. Math. Soc. 15 (1976), 431-438.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Chungnam National University, Taejon, 305-764, South Korea

    Joo Bong Kim, Deok Ho Lee, Woo Youl Lee, Chun-Gil Park & Jae Myung Park

Authors
  1. Joo Bong Kim
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  2. Deok Ho Lee
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  3. Woo Youl Lee
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  4. Chun-Gil Park
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  5. Jae Myung Park
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Kim, J.B., Lee, D.H., Lee, W.Y. et al. The s-Perron, sap-Perron and ap-McShane Integrals. Czechoslovak Mathematical Journal 54, 545–557 (2004). https://doi.org/10.1007/s10587-004-6407-7

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  • DOI: https://doi.org/10.1007/s10587-004-6407-7

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