Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

THE $M_{\alpha}$-INTEGRAL OF BANACH-VALUED FUNCTIONS

  • Park, Jae Myung (Department of Mathematics Chungnam National University) ;
  • Kim, Byung Moo (Department of Mathematics Chungju National University) ;
  • Kim, Young Kuk (Department of Mathematics Education Seowon University) ;
  • Lee, Hoe Kyoung (Department of Mathematics Chungnam National University)
  • Published : 2012.02.15
⟨ Previous Next ⟩

Abstract

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

Keywords

References

  1. B. Bongiorno, Un nvovo interale il problema dell primitive, Le Matematiche, 51 (1996), no. 2, 299-313.
  2. B. Bongiorno, L. Di Piazza, and D. Preiss, A constructive minimal integral which includes Lebesque integrable functions and derivatives, J. London Math. Soc. (2) 62 (2000), no. 1, 117-126. https://doi.org/10.1112/S0024610700008905
  3. A. M. Bruckner, R. J. Fleissner, and J. Fordan, The minimal integral which includeds Lebesque integrable functions and derivatives, Collq. Mat. 50 (1986), 289-293. https://doi.org/10.4064/cm-50-2-289-293
  4. S. J. Chao, B. S. Lee, G. M. Lee, and D. S. Kim, Denjoy-type integrals of Banach-valued functions, Comm. Korean. Math. Soc. 13 (1998), no. 2, 307- 316.
  5. D. H. Fremlin The Henstock and McShane integrals of vector-valued functions, Illinois J. Math. 38 (1994), 471-479.
  6. D. H. Fremlin The McShane, PU and Henstock integrals of Banach valued functions, Cze. J. Math. 52 (127) (2002), 609-633. https://doi.org/10.1023/A:1021736031567
  7. D. H. Fremlin and J. Mendoza, On the integration of vector-valued functions, Illinois J. Math. 38 (1994), 127-147.
  8. R. A. Gordon, The Integrals of Lebegue, Denjoy, Perron, and Henstock, Graduate Studies in Math.4 Amer.Math.Soc. (1994).
  9. R. A. Gordon, The Denjoy extension of the Bochner, Pettis and Dunford integrals, Studia Math. 92 (1989), 73-91. https://doi.org/10.4064/sm-92-1-73-91
  10. R. Henstock, The General Theory of Integration, Oxford University Press, Oxford, 1991.
  11. J. M. Park and D. H. Lee, The Denjoy extension of the Riemann and McShane integrals, Cze J. Math. 50 (2000), no. 125, 615-625. https://doi.org/10.1023/A:1022845929564
  12. L. Di Piazza, A Riemann-type minimal integral for the classical problem of primitives, Rend. Istit. Mat. Univ. Trieste Vol. XXXIV, (2002), 143-153
  13. S. Schwabik and Guoju Ye, Topics in Banach space integration, World Scientific, 2005.
  14. L. P. Yee, Lanzhou Lectures on Henstock Integration, World Scientific, Singapore, 1989.

Cited by

  1. The ℭ-integral of sequence-valued functions on the sequence space ℓ∞ vol.855, 2017, https://doi.org/10.1088/1742-6596/855/1/012028
  2. ON STRONG Mα-INTEGRAL OF BANACH-VALUED FUNCTIONS vol.26, pp.2, 2013, https://doi.org/10.14403/jcms.2013.26.2.259
  3. ON C-DELTA INTEGRAL OF BANACH SPACE VALUED FUNCTIONS ON TIME SCALES vol.29, pp.1, 2016, https://doi.org/10.14403/jcms.2016.29.1.157
  4. THE STRONG $M_{\alpha}$-INTEGRAL OF BANACH-VALUED FUNCTIONS vol.25, pp.4, 2012, https://doi.org/10.14403/jcms.2012.25.4.763