On the Convergence and Iterates of q-Bernstein Polynomials Original Research Article

The convergence properties of q-Bernstein polynomials are investigated. When q⩾1 is fixed the generalized Bernstein polynomials Bnf of f, a one parameter family of Bernstein polynomials, converge to f as n→∞ if f is a polynomial. It is proved that, if the parameter 00, as the number of iterates M→∞. Moreover, the iterates of the Boolean sum of Bnf converge to the interpolating polynomial for f at n+1 geometrically spaced nodes on [0,1].