Some approximation properties of the Kantorovich variant of the Bleimann, Butzer and Hahn operators

Grzegorz Nowak

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 1, page 67-78
  • ISSN: 0010-2628

Abstract

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For some classes of functions f locally integrable in the sense of Lebesgue or Denjoy-Perron on the interval [ 0 ; ∞ ) , the Kantorovich type modification of the Bleimann, Butzer and Hahn operators is considered. The rate of pointwise convergence of these operators at the Lebesgue or Lebesgue-Denjoy points of f is estimated.

How to cite

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Nowak, Grzegorz. "Some approximation properties of the Kantorovich variant of the Bleimann, Butzer and Hahn operators." Commentationes Mathematicae Universitatis Carolinae 49.1 (2008): 67-78. <http://eudml.org/doc/250465>.

@article{Nowak2008,
abstract = {For some classes of functions $f$ locally integrable in the sense of Lebesgue or Denjoy-Perron on the interval $[0;\infty )$, the Kantorovich type modification of the Bleimann, Butzer and Hahn operators is considered. The rate of pointwise convergence of these operators at the Lebesgue or Lebesgue-Denjoy points of $f$ is estimated.},
author = {Nowak, Grzegorz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Bleimann; Butzer and Hahn operator; Lebesgue-Denjoy point; rate of convergence; Lebesgue-Denjoy point; rate of convergence},
language = {eng},
number = {1},
pages = {67-78},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some approximation properties of the Kantorovich variant of the Bleimann, Butzer and Hahn operators},
url = {http://eudml.org/doc/250465},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Nowak, Grzegorz
TI - Some approximation properties of the Kantorovich variant of the Bleimann, Butzer and Hahn operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 1
SP - 67
EP - 78
AB - For some classes of functions $f$ locally integrable in the sense of Lebesgue or Denjoy-Perron on the interval $[0;\infty )$, the Kantorovich type modification of the Bleimann, Butzer and Hahn operators is considered. The rate of pointwise convergence of these operators at the Lebesgue or Lebesgue-Denjoy points of $f$ is estimated.
LA - eng
KW - Bleimann; Butzer and Hahn operator; Lebesgue-Denjoy point; rate of convergence; Lebesgue-Denjoy point; rate of convergence
UR - http://eudml.org/doc/250465
ER -

References

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  4. Abel U., Ivan M., A Kantorovich variant of the Bleimann, Butzer and Hahn operators, Rend. Circ. Mat. Palermo (2) Suppl. (2002), 68 205-218. (2002) Zbl1012.41016MR1975505
  5. Bleimann G., Butzer P.L., Hahn L., A Bernstein-type operator approximating continuous functions of the semi-axis, Indag. Math. 42 (1980), 255-262. (1980) MR0587054
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  7. Della Vecchia B., Some properties of a rational operator of Bernstein-type, in Progress in Approximation Theory (P. Nevai and A. Pinkus, Eds.), Academic Press, New York, 1991, pp.177-185. MR1114772
  8. Hermann T., On the operator of Bleimann, Butzer and Hahn, Colloq. Math. Soc. János Bolyai 58 (1991), 355-360. (1991) Zbl0784.41016MR1211445
  9. Khan R.A., 10.1016/0021-9045(88)90024-X, J. Approx. Theory 53 (1988), 295-303. (1988) Zbl0676.41024MR0947433DOI10.1016/0021-9045(88)90024-X
  10. Khan R.A., Some properties of a Bernstein-type operator of Bleimann, Butzer and Hahn, in Progress in Approximation Theory (P. Nevai and A. Pinkus, Eds.), Academic Press, New York, 1991, pp.497-504. MR1114792
  11. Jayasri C., Sitaraman Y., 10.1016/0377-0427(93)90008-Y, J. Comput. Appl. Math. 47 2 (1993), 267-272. (1993) Zbl0779.41008MR1237316DOI10.1016/0377-0427(93)90008-Y
  12. Nowak G., Pych-Taberska P., Approximation properties of the generalized Favard-Kantorovich operators, Comment. Math. Prace Mat. 39 (1999), 139-152. (1999) Zbl0970.41014MR1739024
  13. Saks S., Theory of the Integral, New York, 1937. Zbl0017.30004
  14. Totik V., Uniform approximation by Bernstein-type operators, Indag. Math. 46 (1984), 87-93. (1984) Zbl0538.41035MR0748982

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