Results 81 to 90 of about 156 (109)

A Quantum Voronovskaya Theorem: Asymptotic Expansions for Quantum Neural Network Operators

We prove the Quantum Voronovskaya--Damasclin Theorem, establishing the first complete asymptotic expansion for Quantum Neural Network Operators (QNNOs) when approximating arbitrary quantum channels. This result generalizes the classical Voronovskaya theorem for Bernstein polynomials to the non‑commutative, multi‑dimensional setting of quantum ...
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A Non-Commutative Voronovskaya Theorem for Quantum Neural Network Operators

We prove a complete asymptotic expansion for quantum neural network operators when they approximate arbitrary quantum channels. This is the non-commutative analogue of the classical Voronovskaya theorem. The expansion reveals that the approximation error splits into three fundamentally different parts: integer powers of \(1/n\) involving ordinary ...
Santos, Rômulo Damasclin Chaves dos, de Andrade, Delvonei Alves   +1 more
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Asymptotic Expansions for Quantum Neural Network Operators: A Non-Commutative Voronovskaya Theorem

We establish a complete asymptotic expansion for Quantum Neural Network Operators (QNNOs) approximating arbitrary quantum channels, providing a non-commutative analogue of the classical Voronovskaya theorem. Within a rigorous functional analytic framework, we introduce quantum Sobolev and Hölder spaces Cm,γ(H) based on Fréchet differentiability in the ...
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Generalized Neural Network Operators with Symmetrized Activations: Fractional Convergence and the Voronovskaya-Damasclin Theorem

17 ...
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A Voronovskaya Type Theorem on Modified Post-Widder Operators Preserving x² [PDF]

Kyungpook mathematical journal, 2011
Mohammad Arif Siddiqui, Raksha Rani Agrawal   +1 more
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A Voronovskaya-type theorem in simultaneous approximation

Periodica Mathematica Hungarica, 2021
A general class of positive linear operators, called exponential type operators, is introduced and studied in [\textit{C. P. May}, Can. J. Math. 28, 1224--1250 (1976; Zbl 0342.41018)] and [\textit{M. E. H. Ismail} and \textit{C. P. May}, J. Math. Anal. Appl.
Adrian Holhos, Holhos Adrian
exaly   +2 more sources

General Voronovskaya and Asymptotic Theorems in Simultaneous Approximation

Mediterranean Journal of Mathematics, 2010
Here the authors prove general asymptotic and Voronovskaya theorems in simultaneous approximation. They generalize the Voronovskaya type result obtained recently by Floater for Bernstein operators and previously by Heilmann and Muller for the Durrmeyer operators.
Heiner Gonska, Radu Păltănea, Păltănea Radu   +2 more
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A Voronovskaya-Type Theorem for the First Derivatives of Positive Linear Operators

Results in Mathematics, 2019
The author considers a family of positive linear operators which satisfy a differential equation similar to the one characterizing the exponential operators of C. P. May. Voronovskaya-type quantitative results for the derivatives of these operators are obtained. The last section is devoted to examples and applications involving modified Szász-Mirakyan,
Adrian Holhos, Holhos Adrian
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Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems

Journal of Applied Mathematics and Computing, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Naim Braha, Hari M Srivastava, Et Mikail   +2 more
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An Elementary Proof of Voronovskaya's Theorem

American Mathematical Monthly, 1975
(1975). An Elementary Proof of Voronovskaya's Theorem. The American Mathematical Monthly: Vol. 82, No. 6, pp. 639-641.
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