• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.643-652
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• 2003

In this paper we introduce the concepts of the Mc-Shane-Stieltjes integral and the Denjoy-McShane-Stieltjes integral for Banach-valued functions and give a characterization of the Mc-Shane-Stieltjes integrability and investigate some properties of the Denjoy-McShane-Stieltjes integral.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.307-316
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• 1998

In this paper Denjoy*-Dunford, Denjoy*-Pettis, Denjoy*-McShane and Denjoy*-Bochner integrals of functions which map an interval [a,b] into a Banach space X are defined. And we give the relations among the integrals.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.137-146
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• 2003

In this paper we introduce the concepts of the weak $Denjoy_*$ integral of real-valued functions and the weak $Denjoy_*$-Dunford, weak $Denjoy_*$-Pettis, weak $Denjoy_*$-Bochner, weak $Denjoy_*$-McShane integrals of Banach-valued functions and then investigate some of their properties.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.315-327
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• 2008

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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.411-417
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• 1996

Some generalizations of the Riemann integral have been studied for real-valued functions. One of these generalizations leads to an integral, often called the McShane integral, that is equivalent to the Lebesgue integral.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.27-39
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• 2007

In this paper, we define and study the C-integral of functions mapping an interval [a,b] into a Banach space X and discuss the relations among Henstock integral, C-integral and McShane integral. We also study the Denjoy extension of the C-integral.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.101-106
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• 1996

In this paper, we will consider the Denjoy-Riemann integral of functions mapping a closed interval into a Banach space. We will show that a Riemann integrable function on [a, b] is Denjoy-Riemann integrable on [a, b] and that a Denjoy-Riemann integrable function on [a, b] is Denjoy-McShane integrable on [a, b].