Abstract : We discuss here recent developments on the convergence of the q-Bernstein polynomials B(sub n)f which replaces the classical Bernstein polynomial with a one parameter family of polynomials. In addition, the convergence of iterates and iterated Boolean sum of q-Bernstein polynomial will be considered. Moreover a q-difference operator D(sub q)f defined by D(sub q)f = fX,QX is applied to q-Bernstein polynomials. This gives us some results which complement those concerning derivatives of Bernstein polynomials. It is shown that, with the parameter 0 is less than q is less than or equal to 1, if the change in k, f(sub r) is greater than or equal to 0 then D(k)(sub q)B(sub n)f is greater than or equal to 0. If f is monotonic so is D(sub q)B(sub n)f. If f is convex then D(2)(sub q)B(sub n)f is greater than or equal to 0.
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