A saturation theorem for combinations of Bernstein-Durrmeyer polynomials

• Autorzy: P. N. Agrawal , Vijay Gupta
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

linear combinations; compact support; inner product

Kategorie tematyczne

• 41A30: Approximation by other special function classes
• 41A36: Approximation by positive operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 2
• Strony: 157-164

Daty

wydano

1992

otrzymano

1991-06-10

poprawiono

1992-02-15

Twórcy

autor

P. N. Agrawal

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

autor

Vijay Gupta

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

Bibliografia

• [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, $L_p$-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.