Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 90, 2011 - Issue 3-4: Approximation Theory and Signal Analysis, a special issue in honour of Professor Paul Leo Butzer
Submit an article Journal homepage
163
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

On the rates of convergence of Bernstein–Chlodovsky polynomials and their Bézier-type variants

Paulina Pych-Taberska Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614, Poznań, Poland
&
Harun Karsli Department of Mathematics, Faculty of Science and Arts, Abant Izzet Baysal University, 14280 Bolu, TurkeyCorrespondence[email protected]
View further author information
Pages 403-416 | Received 21 May 2009, Accepted 07 Oct 2009, Published online: 08 Apr 2010

References

  • Chlodovsky , I . 1937 . Sur le développement des fonctions définies dans un intervalle infini en séries de polynomes de M. S. Bernstein . Compos. Math. , 4 : 380 – 393 .
  • Albrycht , J and Radecki , J . 1960 . On a generalization of the theorem of Voronovskaya, Zeszyty Naukowe UAM , 1 – 7 . Poznań : Zeszyt 2 .
  • Butzer , PL and Karsli , H . 2009 . Voronovskaya-type theorems for derivatives of the Bernstein-Chlodovsky polynomials and the Szász–Mirakyan operator . Comment. Math. , 1 ( 49 ) : 33 – 57 .
  • Bézier , P . 1972 . Numerical Control Mathematics and Applications , London : Wiley .
  • Karsli , H and Ibikli , E . 2007 . Rate of convergence of Chlodovsky type Bernstein operators for functions of bounded variation . Numer. Funct. Anal. Optim. , 28 ( 3–4 ) : 367 – 378 .
  • Karsli , H and Ibikli , E . 2008 . Convergence rate of a new Bézier variant of Chlodovsky operators to bounded variation functions . J. Comput. Appl. Math. , 212 ( 2 ) : 431 – 443 .
  • Chanturiya , ZA . 1974 . Modulus of variation of functions and its application in the theory of Fourier series . Dokl. Akad. Nauk SSSR , 214 : 63 – 66 .
  • Lagrange , MR . 1965 . Sur les oscillations d'ordre supérieur d'une fonction numerique . Ann. Sc. Econ. Norm. Sup. Sér. , 3 ( 82 ) : 101 – 130 .
  • Pych-Taberska , P . 1988 . On the rate of pointwise convergence of Bernstein and Kantorović polynomials . Funct. Approx. , 16 : 63 – 76 .
  • Pych-Taberska , P . 2000 . On the rate of convergence of the Bezier type operators . Funct. Approx. , 28 : 201 – 209 .
  • Pych-Taberska , P . 2003 . Some properties of the Bézier–Kantorovich type operators . J. Approx. Theory , 123 : 256 – 269 .
  • Zeng , XM and Piriou , A . 1998 . On the rate of convergence of two Bernstein–Bézier type operators for bounded variation functions . J. Approx. Theory , 95 : 369 – 387 .
  • Zeng , XM . 2000 . On the rate of convergence of two Bernstein–Bézier type operators for bounded variation functions: II . J. Approx. Theory , 104 : 330 – 344 .
  • Cheng , F . 1983 . On the rate of convergence of Bernstein polynomials of functions of bounded variation . J. Approx. Theory , 39 : 259 – 274 .
  • Bojanic , R . 1979 . An estimate of the rate of convergence for Fourier series of functions of bounded variation . Publ. l'Inst. Math. , 26 : 57 – 60 .
  • Heilmann , M . 1989 . Direct and converse results for operators of Baskakov-Durrmeyer type . Approx. Theory Appl. , 5 ( 1 ) : 105 – 127 .
  • Lorentz , GG . 1953 . Bernstein Polynomials , Toronto : University of Toronto Press .
  • Zeng , XM . 1998 . Bounds for Bernstein basis functions and Meyer–König–Zeller basis functions . J. Math. Anal. Appl. , 219 : 364 – 376 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.