Properties of a new class of recursively defined Baskakov-type operators

Octavian Agratini

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 3, page 353-359
  • ISSN: 0044-8753

Abstract

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By starting from a recent paper by Campiti and Metafune [7], we consider a generalization of the Baskakov operators, which is introduced by replacing the binomial coefficients with other coefficients defined recursively by means of two fixed sequences of real numbers. In this paper, we indicate some of their properties, including a decomposition into an expression which depends linearly on the fixed sequences and an estimation of the corresponding order of approximation, in terms of the modulus of continuity.

How to cite

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Agratini, Octavian. "Properties of a new class of recursively defined Baskakov-type operators." Archivum Mathematicum 034.3 (1998): 353-359. <http://eudml.org/doc/248180>.

@article{Agratini1998,
abstract = {By starting from a recent paper by Campiti and Metafune [7], we consider a generalization of the Baskakov operators, which is introduced by replacing the binomial coefficients with other coefficients defined recursively by means of two fixed sequences of real numbers. In this paper, we indicate some of their properties, including a decomposition into an expression which depends linearly on the fixed sequences and an estimation of the corresponding order of approximation, in terms of the modulus of continuity.},
author = {Agratini, Octavian},
journal = {Archivum Mathematicum},
keywords = {Baskakov-type operators; order of approximation; modulus of continuity; Baskakov-type operators; order of approximation; modulus of continuity},
language = {eng},
number = {3},
pages = {353-359},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Properties of a new class of recursively defined Baskakov-type operators},
url = {http://eudml.org/doc/248180},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Agratini, Octavian
TI - Properties of a new class of recursively defined Baskakov-type operators
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 3
SP - 353
EP - 359
AB - By starting from a recent paper by Campiti and Metafune [7], we consider a generalization of the Baskakov operators, which is introduced by replacing the binomial coefficients with other coefficients defined recursively by means of two fixed sequences of real numbers. In this paper, we indicate some of their properties, including a decomposition into an expression which depends linearly on the fixed sequences and an estimation of the corresponding order of approximation, in terms of the modulus of continuity.
LA - eng
KW - Baskakov-type operators; order of approximation; modulus of continuity; Baskakov-type operators; order of approximation; modulus of continuity
UR - http://eudml.org/doc/248180
ER -

References

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  1. Agratini O., Construction of Baskakov-type operators by wavelets, Rev. d’Analyse Num. et de Théorie de l’Approx., tome 26(1997), 3-10. (1997) Zbl1039.42028MR1703913
  2. Altomare F., Positive projections approximation processes and degenerate diffusion equations, Conf. Sem. Mat. Univ. Bari, 241(1991), 43-68. (1991) Zbl0789.47030MR1185556
  3. Altomare F., Campiti M., Korovkin-type Approximation Theory and its Applications, de Gruyter Studies in Mathematics, Vol. 17, de Gruyter, Berlin/New-York, 1994. (1994) Zbl0924.41001MR1292247
  4. Altomare F., Romanelli S., On some classes of Lototsky-Schnabl operators, Note Mat., 12(1992), 1-13. (1992) Zbl0811.47033MR1258559
  5. Baskakov V. A., An example of a sequence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk SSSR, 113(1957), 249-251 (in Russian). (1957) MR0094640
  6. Campiti M., Limit semigroups of Stancu-Mühlbach operators associated with positive projections, Ann. Sc. Norm. Sup. Pisa, Cl. Sci., 19(1992), 4, 51-67. (1992) Zbl0784.47040MR1183757
  7. Campiti M., Metafune G., Approximation properties of recursively defined Bernstein-type operators, Journal of Approx. Theory, 87(1996), 243-269. (1996) Zbl0865.41027MR1420333
  8. Campiti M., Metafune G., Evolution equations associated with recursively defined Bernstein-type operators, Journal of Approx. Theory, 87(1996), 270-290. (1996) Zbl0874.41010MR1420334
  9. Stancu D. D., Two classes of positive linear operators, Analele Univ. Timişoara, Ser. St. Matem. 8(1970), 213-220. (1970) Zbl0276.41009MR0333538
  10. Stancu D. D., Approximation of functions by means of some new classes of positive linear operators, in “Numerische Methoden der Approximations Theorie”, Vol. 1 (Proc. Conf. Math. Res. Inst., Oberwolfach, 1971; eds. L. Collatz, G. Meinardus), 187-203, Basel: Birkhäuser, 1972. (1971) MR0380207

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