• 충청수학회지
• /
• 제14권1호
• /
• pp.41-48
• /
• 2001

In this paper, we study the sap-Perron and ap-McShane integrals. In particular, we show that the sap-Perron integral is equivalent to the ap-McShane integral.

• 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.

• 대한수학회보
• /
• 제40권1호
• /
• pp.77-83
• /
• 2003

In this paper, we study the strong Perron integral, and show that the strong Perron integral is equivalent to the McShane integral.

• 대한수학회논문집
• /
• 제22권1호
• /
• pp.15-18
• /
• 2007

It is shown that $\alpha-regular$ McShane and strong Perron integrals considered in [1] are equivalent to the usual McShane integral.

• 충청수학회지
• /
• 제13권1호
• /
• pp.21-26
• /
• 2000

In this paper, we define the strong Perron integral and study the relationship between the integrals of strong Perron and McShane.

• 충청수학회지
• /
• 제10권1호
• /
• pp.37-41
• /
• 1997

In this paper, we give a direct proof that the Perron and variational integrals are equivalent.

• 충청수학회지
• /
• 제10권1호
• /
• 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.

• 대한수학회논문집
• /
• 제20권2호
• /
• pp.291-297
• /
• 2005

In this paper, we introduce the SP-integral and the $SP_\alpha-integral$ defined on an interval in the n-dimensional Euclidean space $\mathbb{R}^n$. We also investigate the relationship between these two integrals.

• 대한수학회보
• /
• 제41권2호
• /
• 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 applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.205-228
• /
• 2005

Let I(f) be the integral defined by : $I(f) = \int\limits_{a}^{b} f(x)w(x)dx$ with f a given function, w a nonclassical weight function and [a, b] an interval of IR (of finite or infinite length). We propose to calculate the approximate value of I(f) by using a new scheme for deriving a non-linear system, satisfied by the three-term recurrence coefficients of semi-classical orthogonal polynomials. Finally we studies the Stability and complexity of this scheme.