On modified Meyer-König and Zeller operators of functions of two variables

Lucyna Rempulska; Mariola Skorupka

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 3, page 273-284
  • ISSN: 0044-8753

Abstract

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This paper is motivated by Kirov results on generalized Bernstein polynomials given in (Kirov, G. H., A generalization of the Bernstein polynomials, Math. Balk. New Ser. bf 6 (1992), 147–153.). We introduce certain modified Meyer-König and Zeller operators in the space of differentiable functions of two variables and we study approximation properties for them. Some approximation properties of the Meyer-König and Zeller operators of differentiable functions of one variable are given in (Rempulska, L., Tomczak, K., On certain modified Meyer-König and Zeller operators, Grant PB-43-71/2004.) and (Rempulska, L., Skorupka, M., On strong approximation by modified Meyer-König and Zeller operators, Tamkang J. Math. (in print).).

How to cite

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Rempulska, Lucyna, and Skorupka, Mariola. "On modified Meyer-König and Zeller operators of functions of two variables." Archivum Mathematicum 042.3 (2006): 273-284. <http://eudml.org/doc/249774>.

@article{Rempulska2006,
abstract = {This paper is motivated by Kirov results on generalized Bernstein polynomials given in (Kirov, G. H., A generalization of the Bernstein polynomials, Math. Balk. New Ser. bf 6 (1992), 147–153.). We introduce certain modified Meyer-König and Zeller operators in the space of differentiable functions of two variables and we study approximation properties for them. Some approximation properties of the Meyer-König and Zeller operators of differentiable functions of one variable are given in (Rempulska, L., Tomczak, K., On certain modified Meyer-König and Zeller operators, Grant PB-43-71/2004.) and (Rempulska, L., Skorupka, M., On strong approximation by modified Meyer-König and Zeller operators, Tamkang J. Math. (in print).).},
author = {Rempulska, Lucyna, Skorupka, Mariola},
journal = {Archivum Mathematicum},
keywords = {Meyer-König and Zeller operator; function of two variables; approximation theorem; approximation theorem},
language = {eng},
number = {3},
pages = {273-284},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On modified Meyer-König and Zeller operators of functions of two variables},
url = {http://eudml.org/doc/249774},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Rempulska, Lucyna
AU - Skorupka, Mariola
TI - On modified Meyer-König and Zeller operators of functions of two variables
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 3
SP - 273
EP - 284
AB - This paper is motivated by Kirov results on generalized Bernstein polynomials given in (Kirov, G. H., A generalization of the Bernstein polynomials, Math. Balk. New Ser. bf 6 (1992), 147–153.). We introduce certain modified Meyer-König and Zeller operators in the space of differentiable functions of two variables and we study approximation properties for them. Some approximation properties of the Meyer-König and Zeller operators of differentiable functions of one variable are given in (Rempulska, L., Tomczak, K., On certain modified Meyer-König and Zeller operators, Grant PB-43-71/2004.) and (Rempulska, L., Skorupka, M., On strong approximation by modified Meyer-König and Zeller operators, Tamkang J. Math. (in print).).
LA - eng
KW - Meyer-König and Zeller operator; function of two variables; approximation theorem; approximation theorem
UR - http://eudml.org/doc/249774
ER -

References

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  11. Kirov G. H., A generalization of the Bernstein polynomials, Math. Balk. New Ser. bf 6 (1992), 147–153. (1992) Zbl0838.41017MR1182946
  12. Kirov G. H., Popova L., A generalization of the linear positive operators, Math. Balk. New Ser. 7 (1993), 149–162. (1993) Zbl0833.41016MR1270375
  13. Lupas A., Approximation properties of the M n -operators, Aequationes Math. 5 (1970), 19–37. (1970) MR0279495
  14. Meyer-König W., Zeller K., Bernsteinche Potenzreihen, Studia Math. 19 (1960), 89–94. (1960) MR0111965
  15. Rempulska L., Tomczak K., On certain modified Meyer-König and Zeller operators, Grant PB-43-71/2004. Zbl1107.41018
  16. Rempulska L., Skorupka M., On strong approximation by modified Meyer-König and Zeller operators, Tamkang J. Math. (in print). Zbl1119.41022MR2252622
  17. Timan A. F., Theory of Approximation of Functions of a Real Variable, Moscow, 1960 (Russian). (1960) MR0117478

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