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Article Citation - WoS: 3Citation - Scopus: 5On the Sets of Convergence for Sequences of the q-bernstein Polynomials With q > 1(Hindawi Publishing Corporation, 2012) Ostrovska, Sofiya; Ozban, Ahmet YasarThe aim of this paper is to present new results related to the convergence of the sequence of the q-Bernstein polynomials {B-n,B-q(f x)} in the case q > 1, where f is a continuous function on [0,1]. It is shown that the polynomials converge to f uniformly on the time scale J(q) = {q(-j)}(j-0)(infinity) boolean OR {0}, and that this result is sharp in the sense that the sequence {B-n,B-q(f;x)}(n-1)(infinity) may be divergent for all x is an element of R \ J(q). Further the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper the results are illustrated by numerical examples.
