CONVERGENCE THEOREMS FOR THE C-INTEGRAL

  • 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)
  • Received : 2009.11.05
  • Accepted : 2009.11.25
  • Published : 2010.03.30

Abstract

In this paper, we prove convergence theorems for 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 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 inte- grals, 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, Ox- ford, 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 Scien- tific, 2005.
  14. L. P. Yee, Lanzhou Lectures on Henstock Integration, World Scientific, Singapore, 1989.