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: 0392-4041

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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  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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