On partial derivatives of multivariate Bernstein polynomials [PDF]
, 2016 It is shown that Bernstein polynomials for a multivariate function converge to this function along with partial derivatives provided that the latter derivatives exist and are continuous.
A. N. Shiryaev +17 more
core +2 more sources
Recent progress on univariate and multivariate polynomial and spline quasi-interpolants [PDF]
, 2004 Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform ...
A.T. Diallo +43 more
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On approximation properties of some non-positive Bernstein-Durrmeyer type operators
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper we shall introduce a new type of Bernstein Durrmeyer operators which are not positive on the entire interval [0, 1]. For these operators we will study the uniform convergence on all continuous functions on [0, 1] as well as a result given ...
Vasian Bianca Ioana
doaj +1 more source
Some approximation properties of new ( p , q ) $( p,q ) $ -analogue of Balázs–Szabados operators
Journal of Inequalities and Applications, 2021 In this paper, a new ( p , q ) $( p,q ) $ -analogue of the Balázs–Szabados operators is defined. Moments up to the fourth order are calculated, and second order and fourth order central moments are estimated.
Hayatem Hamal, Pembe Sabancigil
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Asymptotic expansions and Voronovskaja type theorems for the multivariate neural network operators
Mathematical Foundations of Computing, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Costarelli, Danilo, Vinti, Gianluca
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The Bernstein Voronovskaja-type theorem for positive linear approximation operators
Journal of Approximation Theory, 2015 The main result of the paper is a general Bernstein-Voronovskaja property: if \(\{ L_{n} \}_{n\geq 1},\) \(L_{n} : C[0,1] \to C[0,1],\) is a sequence of positive linear approximation operators, i.e., \(L_{n}(f;x) \to f(x)\) as \(n \to \infty\) for \(x \in [0,1],\) and \[ R(L_{n},f,q,x) := L_{n}(f;x) - \sum_{i=0}^{q} L_{n}((\cdot - x)^{i};x) \frac{f^{(i)
Ioan Gavrea, Mircea Ivan
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The Voronovskaja type theorem for an extension of Szász-Mirakjan operators
Demonstratio Mathematica, 2012 Abstract Recently, C. Mortici defined a class of linear and positive operators depending on a certain function ϕ, which generalize the well known Szász-Mirakjan operators. For these generalized operators we establish a Voronovskaja type theorem, the uniform convergence and the order of approximation, using the modulus of continuity.
Pop, Ovidiu T. +2 more
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The q‐Chlodowsky and q‐Szasz‐Durrmeyer Hybrid Operators on Weighted Spaces
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 The main aim of this article is to introduce a new type of q‐Chlodowsky and q‐Szasz‐Durrmeyer hybrid operators on weighted spaces. To this end, we give approximation properties of the modified new q‐Hybrid operators. Moreover, in the weighted spaces, we examine the rate of convergence of the modified new q‐Hybrid operators by means of moduli of ...
Harun Çiçek +2 more
wiley +1 more source
Complete asymptotic expansions related to conjecture on a Voronovskaja-type theorem
Journal of Mathematical Analysis and Applications, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ioan Gavrea, Mircea Ivan
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Convergence and Voronovskaja-type theorems for derivatives of generalized Baskakov operators
Central European Journal of Mathematics, 2008 The authors prove some theorems the convergence of the first derivatives of generalized Baskakov operators for functions of one and two variables in polynomial and exponential weight spaces. Some Voronovskaja-type theorems are also presented.
Wafi Abdul, Khatoon Salma
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