Archiv der Mathematik

, Volume 86, Issue 3, pp 282–288

The approximation by q-Bernstein polynomials in the case q ↓ 1

Authors

    • Department of MathematicsAtilim University
Original Paper

DOI: 10.1007/s00013-005-1503-y

Cite this article as:
Ostrovska, S. Arch. Math. (2006) 86: 282. doi:10.1007/s00013-005-1503-y

Abstract.

Let Bn (f, q; x), n=1, 2, ... , 0 < q < ∞, be the q-Bernstein polynomials of a function f, Bn (f, 1; x) being the classical Bernstein polynomials. It is proved that, in general, {Bn (f, qn; x)} with qn ↓ 1 is not an approximating sequence for fC[0, 1], in contrast to the standard case qn ↓ 1. At the same time, there exists a sequence 0 < δn ↓ 0 such that the condition \(1 \leqq q_{n} \leqq \delta _{n} \) implies the approximation of f by {Bn (f, qn; x)} for all fC[0, 1].

Mathematics Subject Classification (2000).

41A1041A36

Copyright information

© Birkhäuser Verlag, Basel 2006