Abstract
Because all the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange–Hermite interpolation formula, in this paper we obtain semi-discrete quantitative Voronovskaya-type theorems based on various other Lagrange–Hermite interpolation formulas. Applications to Bernstein–Kantorovich and to Bernstein operators are presented.
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