Convergence of Generalized Bernstein Polynomials Original Research Article

Let f∈C[0, 1], q∈(0, 1), and Bn(f, q; x) be generalized Bernstein polynomials based on the q-integers. These polynomials were introduced by G. M. Phillips in 1997. We study convergence properties of the sequence {Bn(f, q; x)}∞n=1. It is shown that in general these properties are essentially different from those in the classical case q=1.