On some properties of the Picard operators

Lucyna Rempulska; Karolina Tomczak

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 2, page 125-135
  • ISSN: 0044-8753

Abstract

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We consider the Picard operators 𝒫 n and 𝒫 n ; r in exponential weighted spaces. We give some elementary and approximation properties of these operators.

How to cite

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Rempulska, Lucyna, and Tomczak, Karolina. "On some properties of the Picard operators." Archivum Mathematicum 045.2 (2009): 125-135. <http://eudml.org/doc/250680>.

@article{Rempulska2009,
abstract = {We consider the Picard operators $\mathcal \{P\}_n$ and $\mathcal \{P\}_\{n;r\}$ in exponential weighted spaces. We give some elementary and approximation properties of these operators.},
author = {Rempulska, Lucyna, Tomczak, Karolina},
journal = {Archivum Mathematicum},
keywords = {Picard operator; exponential weighted space; degree of approximation; Voronovskaya type theorem; Picard operator; exponential weighted space; degree of approximation; Voronovskaya type theorem},
language = {eng},
number = {2},
pages = {125-135},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On some properties of the Picard operators},
url = {http://eudml.org/doc/250680},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Rempulska, Lucyna
AU - Tomczak, Karolina
TI - On some properties of the Picard operators
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 2
SP - 125
EP - 135
AB - We consider the Picard operators $\mathcal {P}_n$ and $\mathcal {P}_{n;r}$ in exponential weighted spaces. We give some elementary and approximation properties of these operators.
LA - eng
KW - Picard operator; exponential weighted space; degree of approximation; Voronovskaya type theorem; Picard operator; exponential weighted space; degree of approximation; Voronovskaya type theorem
UR - http://eudml.org/doc/250680
ER -

References

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  8. Khan, M. K., Vecchia, B. D., Fassih, A., 10.1006/jath.1996.3113, J. Approx. Theory 92 (1998), 22–37. (1998) Zbl0898.41019MR1492856DOI10.1006/jath.1996.3113
  9. Kirov, G. H., A generalization of the Bernstein polynomials, Math. Balkanica (N.S.) 2 (2) (1992), 147–153. (1992) Zbl0838.41017MR1182946
  10. Leśniewicz, A., Rempulska, L., Wasiak, J., Approximation properties of the Picard singular integral in exponential weight spaces, Publ. Mat. 40 (2) (1996), 233–242. (1996) MR1425617
  11. Mohapatra, R. N., Rodriguez, R. S., 10.1002/mana.19901490108, Math. Nachr. 149 (1990), 117–124. (1990) Zbl0726.42003MR1124797DOI10.1002/mana.19901490108
  12. Rempulska, L., Walczak, Z., On modified Picard and Gauss - Weierstrass singular integrals, Ukrain. Math. Zh. 57 (11) (2005), 1577–1584. (2005) Zbl1097.42009MR2221659
  13. Timan, A. F., Theory of Approximation of Functions of a Real Variable, Moscow, 1960, (Russian). (1960) MR0117478

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