THE RELATION BETWEEN HENSTOCK INTEGRAL AND HENSTOCK DELTA INTEGRAL ON TIME SCALES

DOI QR코드

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Park, Jae Myung;Lee, Deok Ho;Yoon, Ju Han;Kim, Young Kuk;Lim, Jong Tae

  • 투고 : 2013.06.19
  • 심사 : 2013.07.16
  • 발행 : 2013.08.15

초록

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 Henstock delta integrable on $[a,b]_{\mathbb{T}}$ if and only if $f^*$ is Henstock integrable on $[a, b]$.

키워드

time scales;Henstock delta integral;${\triangle}$-gauge

참고문헌

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  5. J. M. Park, D. H. Lee, J. H. Yoon, and J. T. Lim, The Henstock and Henstock delta Integrals, Chungcheng J. Math. Soc. 26 (2013), no. 2, 291-298.
  6. A. Perterson and B. Thompson, HenstockCKurzweil Delta and Nabla Integral, J. Math. Anal. Appl. 323 (2006), 162-178. https://doi.org/10.1016/j.jmaa.2005.10.025
  7. Charles W. Swartz, Douglas S Kurtz, Theories of Integration: The Integrals of Riemann Lebesgue, Henstock-Kurzweil, and Mcshane, World Scientific, 2004.
  8. B. S. Thomson, Henstock Kurzweil integtals on time scales, PanAmerican Math J. Vol 18 (2008), no. 1, 1-19.

피인용 문헌

  1. 1. THE RELATION BETWEEN MCSHANE INTEGRAL AND MCSHANE DELTA INTEGRAL vol.27, pp.1, 2014, doi:10.14403/jcms.2013.26.3.625
  2. 2. THE LEBESGUE DELTA INTEGRAL vol.27, pp.3, 2014, doi:10.14403/jcms.2013.26.3.625
  3. 3. CONVERGENCE THEOREMS FOR THE HENSTOCK DELTA INTEGRAL ON TIME SCALES vol.26, pp.4, 2013, doi:10.14403/jcms.2013.26.3.625
  4. 4. THE RIEMANN DELTA INTEGRAL ON TIME SCALES vol.27, pp.2, 2014, doi:10.14403/jcms.2013.26.3.625
  5. 5. THE Mα-DELTA INTEGRAL ON TIME SCALES vol.27, pp.4, 2014, doi:10.14403/jcms.2013.26.3.625

과제정보

연구 과제 주관 기관 : Chungbuk National University