DOI QR코드

DOI QR Code

C-INTEGRAL AND DENJOY-C INTEGRAL

  • Published : 2007.01.31

Abstract

In this paper, we define and study the C-integral of functions mapping an interval [a,b] into a Banach space X and discuss the relations among Henstock integral, C-integral and McShane integral. We also study the Denjoy extension of the C-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 Lebesgue 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 Lebesgue 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 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
  9. R. Henstock, The General Theory of Integration, Oxford University Press, Oxford, 1991
  10. C. K. Park, On Denjoy-McShane-Stieltjes integral, Commun. Korean. Math. Soc. 18 (2003), no. 4, 643-652 https://doi.org/10.4134/CKMS.2003.18.4.643
  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. ON CONVERGENCE THEOREMS FOR THE MCSHANE INTEGRAL ON TIME SCALES vol.25, pp.3, 2012, https://doi.org/10.14403/jcms.2012.25.3.393
  2. 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
  3. ON C-DELTA INTEGRALS ON TIME SCALES vol.25, pp.2, 2012, https://doi.org/10.14403/jcms.2012.25.2.349