Results 1 to 10 of about 672,456 (107)
Approximation properties of λ-Kantorovich operators [PDF]
Journal of Inequalities and Applications, 2018 In the present paper, we study a new type of Bernstein operators depending on the parameter λ∈[−1,1] $\lambda\in[-1,1]$. The Kantorovich modification of these sequences of linear positive operators will be considered.
Ana-Maria Acu +2 more
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The Voronovskaja theorem for Bernstein-Schurer bivariate operators
Journal of Numerical Analysis and Approximation Theory, 2004 The Voronovskaja theorem for the Bernstein-Schurer bivariate operatos is established.
Dan Bărbosu
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Approximation properties of λ-Bernstein operators [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we introduce a new type λ-Bernstein operators with parameter λ∈[−1,1] $\lambda\in[-1,1]$, we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz ...
Qing-Bo Cai, Bo-Yong Lian, Guorong Zhou
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Simultaneous approximation by neural network operators with applications to Voronovskaja formulas [PDF]
Mathematische Nachrichten, Volume 298, Issue 3, Page 871-885, March 2025.In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well‐known neural network (NN) operators activated by the sigmoidal function.
M. Cantarini, Danilo Costarelli
semanticscholar +2 more sources
Voronovskaja-type theorem for modified Bernstein operators
Journal of Mathematical Analysis and Applications, 2021 In this article we study the Voronovskaja-type theorem for modified Bernstein operators which preserve polynomials. As an application we compare modified Bernstein operators in terms of the limit lim n → ∞ B n , h 1 ( x ) ( f , x ) − f ( x ) B n , h 2 (
Jim X. Xiang
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Multivariate Neural Network Operators: Simultaneous Approximation and Voronovskaja‐Type Theorem
Mathematical Methods in the Applied Sciences, Volume 48, Issue 11, Page 10669-10677, 30 July 2025.In this paper, the simultaneous approximation and a Voronoskaja‐type theorem for the multivariate neural network operators of the Kantorovich type have been proved. In order to establish such results, a suitable multivariate Strang–Fix type condition has
M. Cantarini, Danilo Costarelli
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Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators
Journal of Mathematics, 2021 The present study introduces generalized λ-Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions.
Qing-Bo Cai +2 more
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On a Family of Parameter-Based Bernstein Type Operators with Shape-Preserving Properties
Journal of Mathematics, 2023 This article aims to introduce a new linear positive operator with a parameter. Our focus lies in analyzing the distinct characteristics and inherent properties exhibited by this operator.
Bahareh Nouri, Jamshid Saeidian
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Asymptotic expansions and Voronovskaja type theorems for the multivariate neural network operators
Mathematical Foundations of Computing, 2020 In this paper, an asymptotic formula for the so-called multivariate neural network (NN) operators has been established. As a direct consequence, a first and a second order pointwise Voronovskaja type theorem has been reached.
Danilo Costarelli, Gianluca Vinti
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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 ...
Mehmet Ali Özarslan
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