• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.43-51
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• 2002

In this paper we prove a controlled convergence theorem for the Henstock integral by using the new conditions.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.625-630
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• 2013

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 Henstock delta integrable on $[a,b]_{\mathbb{T}}$ if and only if $f^*$ is Henstock integrable on $[a, b]$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.291-298
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• 2012

In this paper we introduce the interval-valued AP- Henstock-Stieltjes integral and investigate some properties of the these integrals.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.745-751
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• 2014

In this paper we introduce the interval-valued Henstock integral on time scales and investigate some properties of these integrals.

• 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.26 no.4
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• pp.879-885
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• 2013

In this paper, we de ne an extension $f^*:[a,b]{\rightarrow}\mathbb{R}$ of function $f^*:[a,b]_{\mathbb{T}}{\rightarrow}\mathbb{R}$ for a time scale ${\mathbb{T}}$ and prove the convergence theorems for the Henstock delta integral on time scales.

• 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.25 no.3
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• pp.393-400
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• 2012

In this paper, we study the process of McShane delta integrals on time scales and discuss the relation between McShane delta integral and Henstock delta integral. We also prove the mono- tone convergence theorem, Fatou's Lemma and the dominated con- vergence theorems for the McShane delta integral.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.71-84
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• 2007

In this paper, we define the C-Stieltjes integral of the functions mapping an interval [a,b] into a Banach space X with respect to g on [a,b], and the C-Stieltjes representable operators for the vector-valued functions which are the generalizations of the Henstock-Stieltjes representable operators. Some properties of the C-Stieltjes operators and the convergence theorems of the C-Stieltjes integral are given.