Generalized Voronovskaja theorem for q-Bernstein polynomials

摘要

We prove a Floater type theorem for the q-Bernstein polynomials, establishing a generalized Voronovskaja theorem. Moreover, a quantitative variant of the obtained generalized Voronovskaja theorem for the q-Bernstein polynomials is also given. As a particular case, we recover the quantitative Voronovskaja theorem established by Videnskii (2005).