DOI QR코드

DOI QR Code

CONVERGENCE THEOREMS FOR THE Mα-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) ;
  • Lim, Jong Tae (Department of Mathematics, Chungnam National University)
  • 투고 : 2011.05.11
  • 심사 : 2011.05.16
  • 발행 : 2011.06.30

초록

In this paper, we investigate some properties of the $M_{\alpha}$-integral and prove convergence theorems for the $M_{\alpha}$-integral.

키워드

과제정보

연구 과제 주관 기관 : Chungju National University

참고문헌

  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.
  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. J. M. Park, Byung Moo Kim, and Young Kuk Kim, Convergence Theorems for the C-integral, Chungcheong J. Math. 23 (2010), (2002), 143-153
  13. L. Di Piazza, A Riemann-type minimal integral for the classical problem of primitives, Rend. Istit. Mat. Univ. Trieste Vol. XXXIV, (2002), 143-153
  14. S. Schwabik and Guoju Ye, Topics in Banach space integration, World Scientific, 2005.
  15. L. P. Yee, Lanzhou Lectures on Henstock Integration, World Scientific, Singa- pore, 1989.