Ostrovska, SofiyaOstrovska, SofiyaOzban, Ahmet YasarÖzban, Ahmet YaşarMathematics2024-07-052024-07-05201231085-337510.1155/2012/1859482-s2.0-84867770903https://doi.org/10.1155/2012/185948https://hdl.handle.net/20.500.14411/1433The 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.eninfo:eu-repo/semantics/openAccess[No Keyword Available]ArticleQ2WOS:000309046100001