Abstract
Using the q-Bernstein basis, we construct a new sequence {L n } of positive linear operators in C[0, 1]. We study its approximation properties and the rate of convergence in terms of modulus of continuity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. G. Kreĭn, M. A. Rutman: Linear operators leaving invariant a cone in a Banach space. Usp. Mat. Nauk (N. S.) 3 (1948), 3–95 (In Russian.); English translation: Amer. Math. Soc. Translation 1950 (1950), 128 pp.
G. Marinescu: Normed Linear Spaces. Academic Press, Bucharest, 1956. (In Romanian.)
S. Ostrovska: The convergence of q-Bernstein polynomials (0 < q < 1) in the complex plane. Math. Nachr. 282 (2009), 243–252.
G. M. Phillips: Bernstein polynomials based on the q-integers. Ann. Numer. Math. 4 (1997), 511–518.
V. S. Videnskii: On the polynomials with respect to the generalized Bernstein basis. In: Problems of modern mathematics and mathematical education, Hertzen readings. St-Petersburg, 2005, pp. 130–134. (In Russian.)
H. Wang, F. Meng: The rate of convergence of q-Bernstein polynomials for 0 < q < 1. J. Approx. Theory 136 (2005), 151–158.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Finta, Z. Approximation by q-Bernstein type operators. Czech Math J 61, 329–336 (2011). https://doi.org/10.1007/s10587-011-0078-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10587-011-0078-y