# On the rate of convergence of the Bézier-type operators

Bollettino dell'Unione Matematica Italiana (2006)

- Volume: 9-B, Issue: 3, page 657-666
- ISSN: 0392-4041

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topAnioł, 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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- BEZIER, P., Numerical Control-Mathematics and Applications, Wiley, London1972.
- 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
- FELLER, W., An Introduction to Probability Theory and its Applications, II, Wiley, New York, 1966. Zbl0138.10207
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- HEILMANN, M., Direct and converse results for operators of Baskakov-Durrmeyer type, Approx. Theory Appl., 5:1 (1989), 105-127. Zbl0669.41014
- PYCH-TABERSKA, P., On the rate of convergence of the Feller operators, Ann. Soc. Math. Pol., Commentat. Math., 31 (1991), 147-156. Zbl0751.60033
- PYCH-TABERSKA, P., On the rate of convergence of the Bézier type operators, Funct. Approximatio, Comment. Math., 28 (2000), 201-209. Zbl0979.41011
- PYCH-TABERSKA, P., Some properties of the Bézier-Kantorovich type operators, Approx. Theory, 123 (2003), 256-269. Zbl1029.41009
- 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
- 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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