Results 101 to 110 of about 553 (125)

New estimates in Voronovskaja’s theorem

Numerical Algorithms, 2011
The author gives a negative answer to a conjecture formulated in [\textit{S. G. Gal}, Mediterr. J. Math. 5, No. 3, 253--272 (2008; Zbl 1185.30039)]: if \(B_{n}(f,x)\) is the Bernstein polynomial of degree \(n,\) then the quantity \(| B_{n}(f,x)-f(x)-\frac{1}{2n} x(1-x)f''(x) |\) is of order \(O(n^{-2}),\) \(n \to \infty,\) for any \(f \in C^{3}[0,1].\)
Gancho Tachev
exaly   +2 more sources

Generalized Voronovskaja theorem for q-Bernstein polynomials

Applied Mathematics and Computation, 2014
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Zoltan Finta
exaly   +2 more sources

Voronovskaja type approximation theorem for q-Szász-beta operators

Applied Mathematics and Computation, 2014
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Ismet Yuksel, Ülkü Dinlemez Kantar
exaly   +4 more sources

A Quantitative Variant of Voronovskaja’s Theorem

Results in Mathematics, 2009
A general quantitative Voronovskaja theorem for Bernstein operators is given which bridges the gap between such estimates in terms of the least concave majorant of the first order modulus of continuity and the first order Ditzian–Totik modulus with classical weight $$\varphi(x) =
Heiner Gonska, Gancho Tachev
exaly   +2 more sources

Voronovskaja-type theorem for modified Bernstein operators

Journal of Mathematical Analysis and Applications, 2021
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exaly   +3 more sources

Voronovskaja Theorem for Simultaneous Approximation by Bernstein Operators on a Simplex

Mediterranean Journal of Mathematics, 2014
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Radu Pǎltǎnea, Gabriel Stan
exaly   +2 more sources

Voronovskaja’s Theorem and Iterations for Complex Bernstein Polynomials in Compact Disks

Mediterranean Journal of Mathematics, 2008
In this paper, firstly we prove the Voronovskaja’s convergence theorem for complex Bernstein polynomials in compact disks in \({\mathbb{C}}\), centered at origin, with quantitative estimates of this convergence. Secondly, we study the approximation properties of the iterates of complex Bernstein polynomials and we prove that they preserve in the unit ...
Sorin G Gal
exaly   +2 more sources

General Form of Voronovskaja’s Theorem in Terms of Weighted Modulus of Continuity

Results in Mathematics, 2015
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Vijay Gupta, Gancho Tachev
exaly   +3 more sources

Voronovskaja Type Approximation Theorem for q-Szasz–Schurer Operators

Springer Proceedings in Mathematics and Statistics, 2016
In 2011, Ozarslan (Miscolc Math Notes, 12:225–235, 2011) introduced the q-Szasz–Schurer operators and investigated their approximation properties. In the present paper, we state the Voronovskaja-type asymptotic formula for q-analogue of Szasz–Schurer operators.
Mehmet Ali Özarslan
exaly   +2 more sources

Voronovskaja Type Theorems and High-Order Convergence Neural Network Operators with Sigmoidal Functions

Mediterranean Journal of Mathematics, 2020
The authors provide an asymptotic formula for neural network (NN for short) operators which are given in terms of sigmoidal functions, i.e., real functions satisfying meaningful assumptions (Theorem 3.1). Also, the authors describe an asymptotic behavior of a finite linear combination of NN type operators (Theorem 4.1).
Danilo Costarelli, Gianluca Vinti
exaly   +3 more sources