• 대한수학회보
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• 제42권3호
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• pp.535-541
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• 2005

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

• 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].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권3호
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• pp.343-351
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• 2008

In this paper, we define the Denjoy and ap-Denjoy integrals of Banach-valued functions, and we investigate some properties of these two integrals. In particular, we show that a Denjoy integrable function is ap-Denjoy integrable.

• 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.