Approximation properties of q-Baskakov operators

• Autorzy: Zoltán Finta , Vijay Gupta
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 41A30: Approximation by other special function classes
• 41A36: Approximation by positive operators
• 41A25: Rate of convergence, degree of approximation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 199-211

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Zoltán Finta

• Babeş-Bolyai University,

autor

Vijay Gupta

• Netaji Subhas Institute of Technology,

Bibliografia

• [1] Andrews G. E., Askey R., Roy R., Special functions, Cambridge Univ. Press, Cambridge, 1999
• [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
• [4] Ditzian Z., Totik V., Moduli of smoothness, Springer, Berlin, 1987
• [5] Phillips G. M., Interpolation and approximation by polynomials, CMS Books in Mathematics, Vol. 14, Springer, Berlin, 2003
• [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

Identyfikatory

DOI

10.2478/s11533-009-0061-0