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- Title
THE RATE OF CONVERGENCE OF q-BERNSTEIN–STANCU POLYNOMIALS.
- Authors
YANJIE JIANG; JUNMING LI
- Abstract
Let q > 0, α ≥ 0, f ∈ C[0, 1], and $B_n^{q,\alpha}(f;x)$ be the q-Bernstein–Stancu polynomials. In the case α = 0, $B_n^{q,\alpha}(f;x)$ reduces to the well-known q-Bernstein polynomials introduced by Phillips in 1997. In this paper, we study the rate of convergence of the sequence $B_n^{q,\alpha}(f;x)$. Both a theorem on convergence and a Voronovskaya-type theorem on the rate of convergence are proved.
- Subjects
BERNSTEIN polynomials; POLYNOMIALS; MATHEMATICAL functions; BOCHNER integrals
- Publication
International Journal of Wavelets, Multiresolution & Information Processing, 2009, Vol 7, Issue 6, p773
- ISSN
0219-6913
- Publication type
Article
- DOI
10.1142/S0219691309003215