• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.61-75
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• 2014

The purpose of this paper is to obtain some integral inequalities with impulses by using the method of Stieltjes derivatives, and we use our results in the study of Lyapunov stability of solutions of a certain nonlinear impulsive integro-differential equation.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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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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• v.6 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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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.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.217-225
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• 1997

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

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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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.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.105-114
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• 2001

In this paper we introduce the concepts of generalized bounded variation with respect to a strictly increasing function and Denjoy-Stieltjes integral of real-valued functions and then prove some properties of them.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.49-56
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• 2008

In this paper, we define the $H_1$ - Stieltjes integral of Banach-valued functions which is a generalization of real-valued $H_1$ - Stieltjes integral and investigate some properties of $H_1$ - Stieltjes integral. Also we show that if $f:[a,b]{\rightarrow}X$ be a function with ${\dim}X\;<\;{\infty}$, then $f{\in}H_1LS([a,b],X,{\alpha})$ if and only if $f{\in}H_1S([a,b],X,{\alpha})$.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.499-509
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• 2008

In this paper we introduce the concepts of the generalized bounded variation in the restricted sense with respect to a strictly increasing function and $Denjoy_*$-Stieltjes integral of real-valued functions and investigate their properties.

• 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.