• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.41-48
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• 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.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.157-162
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• 1999

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

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.77-83
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• 2003

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

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.15-18
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• 2007

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

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.21-26
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• 2000

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

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.37-41
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• 1997

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

• 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.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.291-297
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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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].

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.205-228
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• 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.