On the rate of convergence of the Bézier-type operators

Grażyna Anioł

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 657-666
  • ISSN: 0392-4033

Abstract

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For bounded functions f on an interval I , in particular, for functions of bounded p-th power variation on I there is estimated the rate of pointwise convergence of the Bezier-type modification of the discrete Feller operators. In the main theorem the Chanturiya modulus of variation is used.

How to cite

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Anioł, Grażyna. "On the rate of convergence of the Bézier-type operators." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 657-666. <http://eudml.org/doc/289630>.

@article{Anioł2006,
abstract = {For bounded functions $f$ on an interval $I$, in particular, for functions of bounded p-th power variation on $I$ there is estimated the rate of pointwise convergence of the Bezier-type modification of the discrete Feller operators. In the main theorem the Chanturiya modulus of variation is used.},
author = {Anioł, Grażyna},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {657-666},
publisher = {Unione Matematica Italiana},
title = {On the rate of convergence of the Bézier-type operators},
url = {http://eudml.org/doc/289630},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Anioł, Grażyna
TI - On the rate of convergence of the Bézier-type operators
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 657
EP - 666
AB - For bounded functions $f$ on an interval $I$, in particular, for functions of bounded p-th power variation on $I$ there is estimated the rate of pointwise convergence of the Bezier-type modification of the discrete Feller operators. In the main theorem the Chanturiya modulus of variation is used.
LA - eng
UR - http://eudml.org/doc/289630
ER -

References

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  1. ANIOL, G., On the rate of convergence of some discrete operators, Demonstratio Math., 27 (1994), 367-377. Zbl0817.41023
  2. BEZIER, P., Numerical Control-Mathematics and Applications, Wiley, London1972. 
  3. CHANTURIYA, Z.A., Modulus of variation of function and its application in the theory of Fourier series, Dokl. Akad. Nauk SSSR, 214 (1974), 63-66. Zbl0295.26008
  4. FELLER, W., An Introduction to Probability Theory and its Applications, II, Wiley, New York, 1966. Zbl0138.10207
  5. GUO, S. - KHAN, M.K., On the rate of convergence of some operators on functions of bounded variation, J. Approx. Theory, 58 (1989), 90-101. Zbl0683.41030
  6. HEILMANN, M., Direct and converse results for operators of Baskakov-Durrmeyer type, Approx. Theory Appl., 5:1 (1989), 105-127. Zbl0669.41014
  7. PYCH-TABERSKA, P., On the rate of convergence of the Feller operators, Ann. Soc. Math. Pol., Commentat. Math., 31 (1991), 147-156. Zbl0751.60033
  8. PYCH-TABERSKA, P., On the rate of convergence of the Bézier type operators, Funct. Approximatio, Comment. Math., 28 (2000), 201-209. Zbl0979.41011
  9. PYCH-TABERSKA, P., Some properties of the Bézier-Kantorovich type operators, Approx. Theory, 123 (2003), 256-269. Zbl1029.41009
  10. ZENG, X.M., On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions, II, J. Approx. Theory, 104 (2000), 330-344. Zbl0963.41011
  11. ZENG, X.M. - PIRIOU, A., On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions, J. Approx. Theory, 95 (1998), 369-387. Zbl0918.41016

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