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Galt, S. G.
Annals. Series on mathematics and its applications, 2023, Letnik: 15, Številka: 1-2Journal Article
Since 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 the recent paper Gal 3, I have obtained semi-discrete quantitative Voronovskaya-type theorems based on other Lagrange-Hermite interpolation formulas, like Lagrange interpolation on two and three simple knots and Hermite interpolation on two knots, one simple and the other one double. In the present paper we obtain a semi-discrete quantitative Voronovskaya-type theorem based on Lagrange interpolation on arbitrary p + 1 simple distinct knots.
