We prove a local saturation theorem in ordinary approximation for combinations of Durrmeyer's integral modification of Bernstein polynomials.
@article{bwmeta1.element.bwnjournal-article-apmv57z2p157bwm, author = {P. N. Agrawal and Vijay Gupta}, title = {A saturation theorem for combinations of Bernstein-Durrmeyer polynomials}, journal = {Annales Polonici Mathematici}, volume = {57}, year = {1992}, pages = {157-164}, zbl = {0766.41025}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv57z2p157bwm} }
P. N. Agrawal; Vijay Gupta. A saturation theorem for combinations of Bernstein-Durrmeyer polynomials. Annales Polonici Mathematici, Tome 57 (1992) pp. 157-164. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv57z2p157bwm/
[000] [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). | Zbl 0747.41014
[001] [2] P. N. Agrawal and V. Gupta, Inverse theorem for linear combinations of modified Bernstein polynomials, preprint. | Zbl 0833.41011
[002] [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. | Zbl 0475.41025
[003] [4] Z. Ditzian and K. Ivanov, Bernstein-type operators and their derivatives, ibid. 56 (1989), 72-90.
[004] [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.
[005] [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. | Zbl 0658.41009
[006] [7] C. P. May, Saturation and inverse theorems for combinations of a class of exponential type operators, Canad. J. Math. 28 (1976), 1224-1250. | Zbl 0342.41018
[007] [8] B. Wood, -approximation by linear combinations of integral Bernstein-type operators, Anal. Numér. Théor. Approx. 13 (1) (1984), 65-72.
[008] [9] B. Wood, Uniform approximation by linear combinations of bernstein-type polynomials, J. Approx. Theory 41 (1984), 51-55. | Zbl 0563.41019