• 충청수학회지
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• 제19권2호
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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.

• 충청수학회지
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• 제31권1호
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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.

• 대한수학회보
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• 제41권2호
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• pp.257-267
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• 2004

In this paper, we introduce, for each approximate distribution $\~{T}$ of [a, b], the approximate Henstock-Stieltjes integral with value in Banach spaces. The Henstock integral is a special case of this where $\~{T}\;=\;\{(\tau,\;[a,\;b])\;:\;{\tau}\;{\in}\;[a,\;b]\}$. This new concept generalizes Henstock integral and abstract Perron-Stieltjes integral. We establish a uniform convergence theorem for approximate Henstock-Stieltjes integral, which is an improvement of the uniform convergence theorem for Perron-Stieltjes integral by Schwabik [3].

• 충청수학회지
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• 제10권1호
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• pp.23-28
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• 1997

In this paper, we investigate continuity of $$F(x)=(H){\int}_a^x\;fdG$$ and Henstock-Stieltjes integrability of product of two functions and obtain the formula of integration by parts for the Henstock-Stieltjes integral.

• 충청수학회지
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• 제31권3호
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• pp.333-341
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• 2018

In this paper we introduce the concept of equi-integrability of sequence of the fuzzy number-valued AP-Henstock-Stieltjes integrable functions. Under this concept, we prove two convergence theorems for sequences of the fuzzy number-valued AP-Henstock-Stieltjes integrable functions.

• 충청수학회지
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• 제29권1호
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• pp.109-115
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• 2016

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

• 충청수학회지
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• 제10권1호
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• pp.29-36
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• 1997

In this paper, we verify that Perron, Henstock and variational Stieltjes integrals are all equivalent. That is, a function which is integrable in one sense is integrable in the other sense and their values are all equal.

• Korean Journal of Mathematics
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• 제6권1호
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• pp.87-96
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• 1998

In this paper, we define the Henstock-Stieltjes integral for real-valued function and prove some of its properties.

• 충청수학회지
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• 제32권1호
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• pp.139-147
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• 2019

In this paper we introduce the AP-Henstock-Stieltjes integral for fuzzy-number-valued functions on infinite interval and investigate some properties.

• 충청수학회지
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• 제25권2호
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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.