Let , be the -Bernstein polynomials of a function . It has been known that, in general, the sequence with is not an approximating sequence for , in contrast to the standard case . In this paper, we give the sufficient and necessary condition under which the sequence approximates for any in the case . Based on this condition, we get that if for sufficiently large , then approximates for any . On the other hand, if can approximate for any in the case , then the sequence satisfies .
Xuezhi Wu. "Approximation by -Bernstein Polynomials in the Case ." Abstr. Appl. Anal. 2014 (SI10) 1 - 6, 2014. https://doi.org/10.1155/2014/259491