ArticleOriginal scientific text
Title
A saturation theorem for combinations of Bernstein-Durrmeyer polynomials
Authors 1, 1
Affiliations
- 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
- 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).
- P. N. Agrawal and V. Gupta, Inverse theorem for linear combinations of modified Bernstein polynomials, preprint.
- 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.
- Z. Ditzian and K. Ivanov, Bernstein-type operators and their derivatives, ibid. 56 (1989), 72-90.
- 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.
- 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.
- C. P. May, Saturation and inverse theorems for combinations of a class of exponential type operators, Canad. J. Math. 28 (1976), 1224-1250.
- B. Wood,
-approximation by linear combinations of integral Bernstein-type operators, Anal. Numér. Théor. Approx. 13 (1) (1984), 65-72. - B. Wood, Uniform approximation by linear combinations of bernstein-type polynomials, J. Approx. Theory 41 (1984), 51-55.