• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.2
• /
• pp.177-188
• /
• 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
• /
• v.31 no.1
• /
• pp.151-160
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.257-267
• /
• 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].

• Journal of the Chungcheong Mathematical Society
• /
• v.10 no.1
• /
• pp.23-28
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.3
• /
• pp.333-341
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.1
• /
• pp.109-115
• /
• 2016

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

• Journal of the Chungcheong Mathematical Society
• /
• v.10 no.1
• /
• pp.29-36
• /
• 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
• /
• v.6 no.1
• /
• pp.87-96
• /
• 1998

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

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.1
• /
• pp.139-147
• /
• 2019

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

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

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