• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.177-188
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• 2006

In this paper, we define and study the vector-valued ap-Henstock-Stieltjes integral, we prove the Cauchy extension theorem and the dominated convergence theorems for the ap-Henstock-Stieltjes integral.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.151-157
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• 2017

In this paper we introduce AP-Henstock integral of vector valued functions which is a generalization of Henstock integral of vector valued functions, investigate some of its properties, and characterize AP-Henstock integral of vector valued functions by the notion of equiintegrability.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.41-48
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• 2001

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

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.879-884
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• 2010

In this paper, we introduce the AP-Henstock Dunford, AP-Henstock Pettis and AP-Henstock Bochner integral Banach-valued functions and investigate some properties of the these integrals.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.89-94
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• 2020

In this paper we introduce the concept of the AP-Henstock integral and prove the integration by parts formula for the AP-Henstock integral.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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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].

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.151-160
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• 2018

In this paper we introduce the AP-Henstock-Stieltjes integral for fuzzy-number-valued functions which is an extension of the Henstock-Stieltjes integral and investigate some properties.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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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.