• 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.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.113-121
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• 2014

In this paper, we define an extension $f^*:[a,\;b]{\rightarrow}\mathbb{R}$ of a function $f:[a,\;b]_{\mathbb{T}}{\rightarrow}\mathbb{R}$ for a time scale $\mathbb{T}$ and show that f is McShane delta integrable on $[a,\;b]_{\mathbb{T}}$ if and only if $f^*$ is McShane integrable on [a, b].

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.77-83
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• 2003

In this paper, we study the strong Perron integral, and show that the strong Perron integral is equivalent to the McShane integral.

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.137-143
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• 2000

In this paper, we define the uniformly sequence for the vector valued McShand-Stieltjes integrable functions and prove the dominated convergence theorem for the McShand-Stieltjes integrable functions.

• 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.13 no.1
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• pp.21-26
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• 2000

In this paper, we define the strong Perron integral and study the relationship between the integrals of strong Perron and McShane.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.607-613
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• 2009

In this paper, we define the C-integral and prove the integration by parts formula for the C-integral.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.469-480
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• 2011

Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.349-357
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• 2012

In this paper we introduce the C-delta integral which generalize the McShane delta integral and investigate some properties of these integrals.