Abstract
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.
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References
Andrews G. E., Askey R., Roy R., Special functions, Cambridge Univ. Press, Cambridge, 1999
Aral A., Gupta V., Generalized q-Baskakov operators, preprint
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
Ditzian Z., Totik V., Moduli of smoothness, Springer, Berlin, 1987
Phillips G. M., Interpolation and approximation by polynomials, CMS Books in Mathematics, Vol. 14, Springer, Berlin, 2003
Wang H., Meng F., The rate of convergence of q-Bernstein polynomials for 0 < q < 1, J. Approx. Theory, 2005, 136, 151–158
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Finta, Z., Gupta, V. Approximation properties of q-Baskakov operators. centr.eur.j.math. 8, 199–211 (2010). https://doi.org/10.2478/s11533-009-0061-0
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DOI: https://doi.org/10.2478/s11533-009-0061-0