• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권3호
• /
• pp.315-327
• /
• 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.

• Korean Journal of Mathematics
• /
• 제10권2호
• /
• pp.123-130
• /
• 2002

In this paper we introduce the concepts of Denjoy-Stieltjes-Dunford, Denjoy-Stieltjes-Pettis and Denjoy-Stieltjes-Bochner integrals of Banach-valued functions and then prove some properties of them.

• 대한수학회논문집
• /
• 제18권4호
• /
• pp.643-652
• /
• 2003

In this paper we introduce the concepts of the Mc-Shane-Stieltjes integral and the Denjoy-McShane-Stieltjes integral for Banach-valued functions and give a characterization of the Mc-Shane-Stieltjes integrability and investigate some properties of the Denjoy-McShane-Stieltjes integral.

• 충청수학회지
• /
• 제19권2호
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제14권2호
• /
• pp.71-84
• /
• 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.

• 충청수학회지
• /
• 제28권1호
• /
• pp.53-63
• /
• 2015

In this paper, we define and study the Riemann-Stieltjes diamond-alpha integral on time scales. Many properties of this integral will be obtained. The Riemann-Stieltjes diamond-alpha integral contains the Riemann{Stieltjes integral and diamond-alpha integral as special cases.

• 충청수학회지
• /
• 제12권1호
• /
• pp.157-162
• /
• 1999

In this paper, we introduce approximate Perron-Stieltjes integral and approximate Roussel derivative and investigate the differentiability of indefinite approximate Perron-Stieltjes integral.

• Journal of applied mathematics & informatics
• /
• 제7권3호
• /
• pp.843-859
• /
• 2000

An Ostrowski type integral inequality for the Riemann-Stieltjes integral ${\int^b}_a$ f(t) du(t), where f is assumed to be of bounded variation on [a, b] and u is of r - H - $H\"{o}lder$ type on the same interval, is given. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.

• 충청수학회지
• /
• 제31권1호
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제8권2호
• /
• pp.87-99
• /
• 2001

In this paper, we define the Mcshane-Stieltjes integral for Banach-valued functions, and will investigate some of its properties and comparison with the Pettis integral.