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The Denjoy*-Stieltjes Extension of the Bochner, Dunford, Pettis and McShane Integrals

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In this paper we introduce the concepts of Denjoy¤-Stieltjes-Dunford, Denjoy¤-Stieltjes-Pettis, Denjoy¤-Stieltjes-Bochner and Denjoy¤-McShane-Stieltjes integrals of Banach-valued functions using the Denjoy¤-Stieltjes integral of real-valued functions and investigate their properties.

Abstract

In this paper we introduce the concepts of Denjoy¤-Stieltjes-Dunford, Denjoy¤-Stieltjes-Pettis, Denjoy¤-Stieltjes-Bochner and Denjoy¤-McShane-Stieltjes integrals of Banach-valued functions using the Denjoy¤-Stieltjes integral of real-valued functions and investigate their properties.

참고문헌 (9)

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  2. J.L. Gamez, "On Denjoy-Dunford and Denjoy-Pettis integrals", Studia Math, 130(1-2), pp.115~133 (1998)
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  4. "The integrals of Lebesgue, Denjoy, Perron and Henstock. Grad. Stud. Math. 4, Amer. Math. Soc., Providence, R.I.", ~ (1994)
  5. :The McShane integral of Banach-valued functions.Illinois J.Math.34, "The McShane integral of Banach-valued functions", Illinois J. Math, 34(3), pp.557~567 (1990)
  6. S. Hu, "Some Remarks on Generalized Riemann Integral", J. Math. Anal. Appl, 137, pp.515~527 (1989)
  7. C.K. Park, "On Denjoy¤-Stieltjes integral", ~
  8. J.M. Park, "The Denjoy extension of the McShane integral", Bull. Korean Math. Soc, 33(3), pp.411~417 (1996)
  9. S. Saks, "Theory of the integral" (1964), Dover

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