Inverse results for generalized Favard-Kantorovich and Favard-Durrmeyer operators in weighted function spaces

Nowak Grzegorz

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 1, page 183-195
  • ISSN: 0392-4033

Abstract

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We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove inverse approximation theorems for functions f such that w 2 m f L p ( R ) , where 1 p and w 2 m ( x ) = ( 1 + x 2 m ) - 1 , m N 0 .

How to cite

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Grzegorz, Nowak. "Inverse results for generalized Favard-Kantorovich and Favard-Durrmeyer operators in weighted function spaces." Bollettino dell'Unione Matematica Italiana 9-B.1 (2006): 183-195. <http://eudml.org/doc/289616>.

@article{Grzegorz2006,
abstract = {We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove inverse approximation theorems for functions \(f\) such that \(w\_\{2m\} f \in L^p (R)\), where \(1\leq p \leq \infty\) and \(w\_\{2m\}(x)=(1+ x^\{2m\})^\{-1\}\), $m \in N_0$.},
author = {Grzegorz, Nowak},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {183-195},
publisher = {Unione Matematica Italiana},
title = {Inverse results for generalized Favard-Kantorovich and Favard-Durrmeyer operators in weighted function spaces},
url = {http://eudml.org/doc/289616},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Grzegorz, Nowak
TI - Inverse results for generalized Favard-Kantorovich and Favard-Durrmeyer operators in weighted function spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/2//
PB - Unione Matematica Italiana
VL - 9-B
IS - 1
SP - 183
EP - 195
AB - We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove inverse approximation theorems for functions \(f\) such that \(w_{2m} f \in L^p (R)\), where \(1\leq p \leq \infty\) and \(w_{2m}(x)=(1+ x^{2m})^{-1}\), $m \in N_0$.
LA - eng
UR - http://eudml.org/doc/289616
ER -

References

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  1. BECKER, M. - BUTZER, P.L. - NESSEL, R.J., Saturation for Favard operators in weighted function spaces, Studia Math., 59 (1976), 139-153. Zbl0352.41023MR438006DOI10.4064/sm-59-2-139-153
  2. BECKER, M., Inverse theorems for Favard operators in polynomial weight spaces,Ann. Soc. Math. Pol., Ser. I: Comment Math., 22 (1981), 165-173. Zbl0508.41017MR641432
  3. BERENS, H. - LORENTZ, G.G., Inverse theorems for Bernstein polynomials, Indiana University Mathematics Journal, Vol. 21, No 8 (1972). Zbl0262.41006MR296579DOI10.1512/iumj.1972.21.21054
  4. BUTZER, P.L. - NESSEL, R.J., Fourier Analysis and Approximation, Vol. I, Academic Press, New York and London, 1971. Zbl0217.42603MR510857
  5. DITZIAN, Z. - TOTIK, V., Moduli of Smoothness, Springer Series in Computational Mathematics, Vol. 9, Springer-Verlag, New York Inc., 1987. MR914149DOI10.1007/978-1-4612-4778-4
  6. FAVARD, J., Sur les multiplicateurs d'interpolation, J. Math. Pures Appl., 23 (1944),219-247. Zbl0063.01317MR15547
  7. GAWRONSKI, W. - STADTMULLER, U., Approximation of continuous functions by generalized Favard operators, J. Approx. Theory, 34 (1982), 384-396. Zbl0484.41019MR656639DOI10.1016/0021-9045(82)90081-8
  8. NOWAK, G., Direct results for generalized Favard-Kantorovich and Favard-Durrmeyer operators in weighted function spaces. Demonstratio Math., 36 (2003), 879-891. Zbl1044.41011MR2018708
  9. NOWAK, G. - PYCH-TABERSKA, P., Approximation properties of the generalized Favard-Kantorovich operators, Ann. Soc. Math. Pol., Ser. I: Comment. Math., 39 (1999), 139-152. Zbl0970.41014MR1739024
  10. NOWAK, G. - PYCH-TABERSKA, P., Some properties of the generalized Favard Durrmeyer operators, Funct. et Approximatio, Comment. Math., 29 (2001), 103-112. MR2135601
  11. PYCH-TABERSKA, P., On the generalized Favard operators, Funct. Approximatio, Comment. Math., 26 (1998), 256-273. Zbl0920.41009MR1666626

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