• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.259-268
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• 2013

In this paper, we define the Banach-valued strong $M_{\alpha}$-integral and study the primitive of the strong $M_{\alpha}$-integral in terms of the $M_{\alpha}$-variational measures. We also prove that every function of bounded variation is a multiplier for the strong $M_{\alpha}$-integral.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.99-108
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• 2010

In this paper, we define the $M_{\alpha}$-integral and investigate properties of the $M_{\alpha}$-integral.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.41-46
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• 2003

In this paper, we investigate the $SP_{\alpha}$-integral and the $M_{\alpha}$-integral defined on an interval of the n-dimensional Euclidean space $\mathbb{R}^n$. In particular, we show that these two integrals are equivalent.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.763-769
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• 2012

In this paper, we define the strong $M_{\alpha}$-integral of Banach-valued functions and investigate some properties of the strong $M_{\alpha}$-integral.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.115-125
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• 2012

In this paper, we define the $M_{\alpha}$-integral of Banach-valued functions and investigate some properties of the $M_{\alpha}$-integral.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.383-391
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• 2011

In this paper, we investigate some properties of the $M_{\alpha}$-integral and prove convergence theorems for the $M_{\alpha}$-integral.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.861-870
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• 2010

In this paper, we define the $M_{\alpha}$-integral and prove the integration by parts formula for the $M_{\alpha}$-integral.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.661-674
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• 2014

In this paper, we define the $M_{\alpha}$-delta integral and investigate the relation between the $M_{\alpha}$ and $M_{\alpha}$-delta integrals on time scales.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.469-480
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• 2011

Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.

• The Pure and Applied Mathematics
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• v.11 no.3
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• pp.189-196
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• 2004

In this article, using the L'Hospital rule, mathematical induction, the trigonometric power formulae and integration by parts, some integral formulae for the improper integrals ${\int}_0^{\infty}$[sin$^{2m}({\alpha}x)]/(x^{2n})dx$ AND ${\int}_0^{\infty}$[sin$^{2m+1}({\alpha}x)]/(x^{2n+1})dx$ are established, where m $\geq$ n are all positive integers and $\alpha$$\neq$ 0.