• Title/Summary/Keyword: $M_{\alpha}$-integral

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ON STRONG Mα-INTEGRAL OF BANACH-VALUED FUNCTIONS

  • You, Xuexiao;Cheng, Jian;Zhao, Dafang
    • 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.

THE Mα-INTEGRAL

  • Park, Jae Myung;Ryu, Hyung Won;Lee, Hoe Kyoung
    • 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.

THE n-DIMENSIONAL SPα AND Mα-INTEGRALS

  • Park, Jae-Myung
    • 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.

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CHARACTERIZING CONVERGENCE CONDITIONS FOR THE Mα-INTEGRAL

  • Garces, Ian June Luzon;Racca, Abraham Perral
    • 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.

EVALUATIONS OF THE IMPROPER INTEGRALS ${\int}_0^{\infty}$[sin$^{2m}({\alpha}x)]/(x^{2n})dx$ AND ${\int}_0^{\infty}$[sin$^{2m+1}({\alpha}x)]/(x^{2n+1})dx$

  • Qi, Feng;Luo, Qiu-Ming;Guo, Bai-Ni
    • 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.

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