# Approximation properties of q-Baskakov operators

Open Mathematics (2010)

- Volume: 8, Issue: 1, page 199-211
- ISSN: 2391-5455

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topZoltán Finta, and Vijay Gupta. "Approximation properties of q-Baskakov operators." Open Mathematics 8.1 (2010): 199-211. <http://eudml.org/doc/269602>.

@article{ZoltánFinta2010,

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.},

author = {Zoltán Finta, Vijay Gupta},

journal = {Open Mathematics},

keywords = {q-Baskakov operator; Ditzian-Totik modulus of smoothness; K-functional; -Baskakov operator; -functional},

language = {eng},

number = {1},

pages = {199-211},

title = {Approximation properties of q-Baskakov operators},

url = {http://eudml.org/doc/269602},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Zoltán Finta

AU - Vijay Gupta

TI - Approximation properties of q-Baskakov operators

JO - Open Mathematics

PY - 2010

VL - 8

IS - 1

SP - 199

EP - 211

AB - 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.

LA - eng

KW - q-Baskakov operator; Ditzian-Totik modulus of smoothness; K-functional; -Baskakov operator; -functional

UR - http://eudml.org/doc/269602

ER -

## References

top- [1] Andrews G. E., Askey R., Roy R., Special functions, Cambridge Univ. Press, Cambridge, 1999 Zbl0920.33001
- [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 Zbl0080.05201
- [4] Ditzian Z., Totik V., Moduli of smoothness, Springer, Berlin, 1987 Zbl0666.41001
- [5] Phillips G. M., Interpolation and approximation by polynomials, CMS Books in Mathematics, Vol. 14, Springer, Berlin, 2003 Zbl1023.41002
- [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 Zbl1082.41007

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