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Article Citation - WoS: 17Citation - Scopus: 16The Approximation by q-bernstein Polynomials in the Case q ↓ 1(Springer Basel Ag, 2006) Ostrovska, SLet B-n (f, q; x), n = 1, 2, ... , 0 < q < infinity, be the q-Bernstein polynomials of a function f, B-n (f, 1; x) being the classical Bernstein polynomials. It is proved that, in general, {B-n (f, q(n); x)} with q(n) down arrow 1 is not an approximating sequence for f is an element of C[0, 1], in contrast to the standard case q(n) up arrow 1. At the same time, there exists a sequence 0 < delta(n) down arrow 0 such that the condition 1 <= q(n) <= delta(n) implies the approximation of f by {B-n(f, qn; x)} for all f is an element of C[0, 1].
