A saturation theorem for combinations of Bernstein-Durrmeyer polynomials

P. N. Agrawal; Vijay Gupta

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 2, page 157-164
  • ISSN: 0066-2216

Abstract

top
We prove a local saturation theorem in ordinary approximation for combinations of Durrmeyer's integral modification of Bernstein polynomials.

How to cite

top

P. N. Agrawal, and Vijay Gupta. "A saturation theorem for combinations of Bernstein-Durrmeyer polynomials." Annales Polonici Mathematici 57.2 (1992): 157-164. <http://eudml.org/doc/262423>.

@article{P1992,
abstract = {We prove a local saturation theorem in ordinary approximation for combinations of Durrmeyer's integral modification of Bernstein polynomials.},
author = {P. N. Agrawal, Vijay Gupta},
journal = {Annales Polonici Mathematici},
keywords = {linear combinations; compact support; inner product; Bernstein-Durrmeyer polynomials; Bernstein-Durrmeyer operators},
language = {eng},
number = {2},
pages = {157-164},
title = {A saturation theorem for combinations of Bernstein-Durrmeyer polynomials},
url = {http://eudml.org/doc/262423},
volume = {57},
year = {1992},
}

TY - JOUR
AU - P. N. Agrawal
AU - Vijay Gupta
TI - A saturation theorem for combinations of Bernstein-Durrmeyer polynomials
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 2
SP - 157
EP - 164
AB - We prove a local saturation theorem in ordinary approximation for combinations of Durrmeyer's integral modification of Bernstein polynomials.
LA - eng
KW - linear combinations; compact support; inner product; Bernstein-Durrmeyer polynomials; Bernstein-Durrmeyer operators
UR - http://eudml.org/doc/262423
ER -

References

top
  1. [1] P. N. Agrawal and V. Gupta, Simultaneous approximation by linear combination of the modified Bernstein polynomials, Bull. Soc. Math. Grèce 30 (1989), 21-29 (1990). Zbl0747.41014
  2. [2] P. N. Agrawal and V. Gupta, Inverse theorem for linear combinations of modified Bernstein polynomials, preprint. Zbl0833.41011
  3. [3] M. M. Derriennic, Sur l'approximation de fonctions intégrables sur [0,1] par des polynômes de Bernstein modifiés, J. Approx. Theory 31 (1981), 325-343. Zbl0475.41025
  4. [4] Z. Ditzian and K. Ivanov, Bernstein-type operators and their derivatives, ibid. 56 (1989), 72-90. 
  5. [5] J. L. Durrmeyer, Une formule d'inversion de la transformée de Laplace: Application à la théorie des moments, Thèse de 3e cycle, Faculté des Sciences de l'Université de Paris, 1967. 
  6. [6] H. S. Kasana and P. N. Agrawal, On sharp estimates and linear combinations of modified Bernstein polynomials, Bull. Soc. Math. Belg. Sér. B 40 (1) (1988), 61-71. Zbl0658.41009
  7. [7] C. P. May, Saturation and inverse theorems for combinations of a class of exponential type operators, Canad. J. Math. 28 (1976), 1224-1250. Zbl0342.41018
  8. [8] B. Wood, L p -approximation by linear combinations of integral Bernstein-type operators, Anal. Numér. Théor. Approx. 13 (1) (1984), 65-72. 
  9. [9] B. Wood, Uniform approximation by linear combinations of bernstein-type polynomials, J. Approx. Theory 41 (1984), 51-55. Zbl0563.41019

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.