Abstract
A gap between saturation and direct-converse theorems for Kantoro-vich-Bernstein polynomials will be closed for a steady rate of convergence. The present theorems unify the above-mentioned results. Furthermore, it is shown that for steady rates our converse results are an improvement on both weak-type converse theorems and strong-weak-type converse theorems for the Kantorovich-Bernstein polynomials.
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Communicated by George G. Lorentz.AMS classification: 41A27, 41A36, 41A40.
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Ditzian, Z., Zhou, X. Kantorovich-Bernstein polynomials. Constr. Approx 6, 421–435 (1990). https://doi.org/10.1007/BF01888273
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DOI: https://doi.org/10.1007/BF01888273