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We represent new estimates of errors of quadrature formula, formula of numerical differentiation and approximation using Taylor polynomial. To measure the errors we apply representation of the remainder in Taylor formula by least concave majorant of the modulus of continuity of the n−th derivative of an n−times differentiable function. Our quantitative(More)
We consider the question if lower estimates in terms of the second order Ditzian-Totik modulus are possible, when we measure the pointwise approximation of continuous function by Bernstein operator. In this case we confirm the conjecture made by Cao, Gonska and Kacsó. To prove this we first establish sharp upper and lower bounds for pointwise approximation(More)
In this paper we represent new quantitative variants of Voronovskaja's Theorem for Schoenberg variation-diminishing spline operator. We estimate the rate of uniform convergence for f ∈ C 2 [0,1] and generalize the results obtained earlier On variation-diminishing Schoenberg operators: new quantitative statements, Multivariate Approximation and Interpoltaion(More)
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