The aim of this paper is to present new results related to the convergence of the sequence of the -Bernstein polynomials in the case , where is a continuous function on . It is shown that the polynomials converge to uniformly on the time scale , and that this result is sharp in the sense that the sequence may be divergent for all . Further, the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper, the results are illustrated by numerical examples.
"On the Sets of Convergence for Sequences of the -Bernstein Polynomials with ." Abstr. Appl. Anal. 2012 1 - 19, 2012. https://doi.org/10.1155/2012/185948