Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE RELATION BETWEEN MCSHANE INTEGRAL AND MCSHANE DELTA INTEGRAL

  • Park, Jae Myung (Department of Mathematics Chungnam National University) ;
  • Lee, Deok Ho (Department of Mathematics Education KongJu National University) ;
  • Yoon, Ju Han (Department of Mathematics Education Chungbuk National University) ;
  • Kim, Young Kuk (Department of Mathematics Education Seowon University) ;
  • Lim, Jong Tae (Department of Mathematics Chungnam National University)
  • Received : 2013.12.24
  • Accepted : 2014.01.16
  • Published : 2014.02.15
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Abstract

In this paper, we define an extension $f^*:[a,\;b]{\rightarrow}\mathbb{R}$ of a function $f:[a,\;b]_{\mathbb{T}}{\rightarrow}\mathbb{R}$ for a time scale $\mathbb{T}$ and show that f is McShane delta integrable on $[a,\;b]_{\mathbb{T}}$ if and only if $f^*$ is McShane integrable on [a, b].

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References

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  1. THE Mα-DELTA INTEGRAL ON TIME SCALES vol.27, pp.4, 2014, https://doi.org/10.14403/jcms.2014.27.4.661
  2. THE RIEMANN DELTA INTEGRAL ON TIME SCALES vol.27, pp.2, 2014, https://doi.org/10.14403/jcms.2014.27.2.327
  3. THE LEBESGUE DELTA INTEGRAL vol.27, pp.3, 2014, https://doi.org/10.14403/jcms.2014.27.3.489