关键词:  q-Bernstein polynomial, acceleration, iterated Boolean sum, convergence rate

Abstract: In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn(f,q;x) to B∞(f,q;x) but also the convergence of their iterated Boolean sum. Using the methods of exact estimate and theories of modulus of smoothness, we get the respective estimates of the convergence rate, which suggest that q-Bernstein polynomials have the similar answer with the classical Bernstein polynomials to these two problems.

Key words:  q-Bernstein polynomial, acceleration, iterated Boolean sum, convergence rate