ArticleOriginal scientific text

Title

A saturation theorem for combinations of Bernstein-Durrmeyer polynomials

Authors 1, 1

Affiliations

  1. Department of Mathematics, University of Roorkee, Roorkee 247667, U.P., India

Abstract

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

Keywords

linear combinations, compact support, inner product

Bibliography

  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).
  2. P. N. Agrawal and V. Gupta, Inverse theorem for linear combinations of modified Bernstein polynomials, preprint.
  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.
  4. Z. Ditzian and K. Ivanov, Bernstein-type operators and their derivatives, ibid. 56 (1989), 72-90.
  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. 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.
  7. C. P. May, Saturation and inverse theorems for combinations of a class of exponential type operators, Canad. J. Math. 28 (1976), 1224-1250.
  8. B. Wood, Lp-approximation by linear combinations of integral Bernstein-type operators, Anal. Numér. Théor. Approx. 13 (1) (1984), 65-72.
  9. B. Wood, Uniform approximation by linear combinations of bernstein-type polynomials, J. Approx. Theory 41 (1984), 51-55.
Pages:
157-164
Main language of publication
English
Received
1991-06-10
Accepted
1992-02-15
Published
1992
Exact and natural sciences