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We establish quantitative Voronovskaja type theorems for the q-Bernstein operators introduced by Phillips in 1997. Our estimates are given with the aid of the first order Ditzian-Totik modulus of smoothness.

Mathematics Subject Classification (2010): 41A10, 41A25, 41A36.

Keywords: Voronovskaja theorem, q-integers, q-Bernstein operators, Kfunctional,first order Ditzian-Totik modulus of smoothness.