• 충청수학회지
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• 제20권4호
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• pp.543-550
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• 2007

In this paper, we define the ap-Denjoy integral and investigate some properties od the ap-Denjoy integral. In particular, we show that a function f : [a,b]${\rightarrow}\mathbb{R}$ is ap-Denjoy integrable on [a,b] if and only if there exists an $ACG_s$ function F on [a,b] such that $F^{\prime}_{ap}=f$ almost everywhere on [a,b].

• Korean Journal of Mathematics
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• 제9권2호
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• pp.105-114
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• 2001

In this paper we introduce the concepts of generalized bounded variation with respect to a strictly increasing function and Denjoy-Stieltjes integral of real-valued functions and then prove some properties of them.

• 충청수학회지
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• 제17권1호
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• pp.103-110
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• 2004

In this paper, we define the ap-Denjoy integral and investigate some properties of the ap-Denjoy integral.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.499-509
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• 2008

In this paper we introduce the concepts of the generalized bounded variation in the restricted sense with respect to a strictly increasing function and $Denjoy_*$-Stieltjes integral of real-valued functions and investigate their properties.

• 충청수학회지
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• 제21권1호
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• pp.79-89
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• 2008

In this paper, we define the ap-Henstock integral and the ap-Denjoy integral of Banach-valued functions, and we investigate some properties of these two integrals. In particular, we show that the ap-Henstock integral is equivalent to the ap-Denjoy integral.

• 충청수학회지
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• 제9권1호
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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].

• 대한수학회보
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• 제33권3호
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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.