论文信息 - Saturation of convergence for q-Bernstein polynomials in the case q ≥ 1

Saturation of convergence for q-Bernstein polynomials in the case q ≥ 1

Abstract In the note, we discuss Voronovskaya type theorem and saturation of convergence for q-Bernstein polynomials for a function analytic in the disc U R : = { z : | z | R } ( R > q ) for arbitrary fixed q ⩾ 1 . We give explicit formulas of Voronovskaya type for the q-Bernstein polynomials for q > 1 . We show that the rate of convergence for the q-Bernstein polynomials is o ( q − n ) ( q > 1 ) for infinite number of points having an accumulation point on U R / q if and only if f is linear.

Wang Heping | XueZhi Wu

[1] Sofiya Ostrovska. The approximation by q-Bernstein polynomials in the case q ↓ 1 , 2006 .

[2] Sofiya Ostrovska,et al. On the improvement of analytic properties under the limit q-Bernstein operator , 2006, J. Approx. Theory.

[3] Sofiya Ostrovska,et al. Convergence of Generalized Bernstein Polynomials , 2002, J. Approx. Theory.

[4] Heping Wang,et al. The rate of convergence of q-Bernstein polynomials for 0 , 2005, J. Approx. Theory.

[5] Sofiya Ostrovska,et al. q-Bernstein polynomials and their iterates , 2003, J. Approx. Theory.

[6] G. Phillips. Interpolation and Approximation by Polynomials , 2003 .

[7] Heping Wang,et al. Voronovskaya-type formulas and saturation of convergence for q-Bernstein polynomials for 0 , 2007, J. Approx. Theory.

[8] Wang Heping. Korovkin-type theorem and application , 2005 .

[9] Halil Oruç,et al. On the q-Bernstein Polynomials , 2001 .

[10] Victor S. Videnskii. On Some Classes of q-parametric Positive linear Operators , 2005 .

[11] V S Videnskii. ON SOME CLASSES OF Q-PARAMETRIC POSITIVE OPERATORS , 2005 .