We establish direct estimates for the q-Baskakov operator introduced by Aral and Gupta in [2], using the second order Ditzian-Totik modulus of smoothness. Furthermore, we define and study the limit q-Baskakov operator.
@article{bwmeta1.element.doi-10_2478_s11533-009-0061-0,
author = {Zolt\'an Finta and Vijay Gupta},
title = {Approximation properties of q-Baskakov operators},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {199-211},
zbl = {1185.41021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0061-0}
}
Zoltán Finta; Vijay Gupta. Approximation properties of q-Baskakov operators. Open Mathematics, Tome 8 (2010) pp. 199-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0061-0/
[1] Andrews G. E., Askey R., Roy R., Special functions, Cambridge Univ. Press, Cambridge, 1999 | Zbl 0920.33001
[2] Aral A., Gupta V., Generalized q-Baskakov operators, preprint
[3] Baskakov V. A., An example of sequence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk. SSSR, 1957, 113, 249–251 | Zbl 0080.05201
[4] Ditzian Z., Totik V., Moduli of smoothness, Springer, Berlin, 1987 | Zbl 0666.41001
[5] Phillips G. M., Interpolation and approximation by polynomials, CMS Books in Mathematics, Vol. 14, Springer, Berlin, 2003 | Zbl 1023.41002
[6] Wang H., Meng F., The rate of convergence of q-Bernstein polynomials for 0 < q < 1, J. Approx. Theory, 2005, 136, 151–158 http://dx.doi.org/10.1016/j.jat.2005.07.001 | Zbl 1082.41007