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

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

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 f ∈C[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 f ∈C[0, 1].

Sofiya Ostrovska

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