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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)

- GANCHO TACHEV, I. Gavrea
- 2009

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)

- Heiner Gonska, Jürgen Prestin, Gancho Tachev
- Appl. Math. Lett.
- 2013

In this work we discuss the rate of simultaneous approximation of Hölder continuous functions by Bernstein operators, measured by Hölder norms with different exponents. We extend the known results on this topic.

- Maria Daniela Rusu, Heiner Gonska, Gancho Tachev, Maria Daniela RUSU
- 2014

- Gancho Tachev
- Computers & Mathematics with Applications
- 2011

- Gancho T. Tachev
- 2012

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)

- Gancho Tachev
- Numerical Algorithms
- 2011

In the present article we establish pointwise variant of E. V. Voronovskaja’s 1932 result, concerning the degree of approximation of Bernstein operator, applied to functions f ∈ C 3[0, 1].

- GANCHO TACHEV
- 2012

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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