Voronovskaja-type results in compact disks for quaternion \(q\)-Bernstein operators, \(q\geq 1\)

DOI10.1007/S11785-011-0213-7zbMath1282.41005OpenAlexW2028070254MaRDI QIDQ371673

Sorin Gheorghe Gal

Publication date: 10 October 2013

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-011-0213-7

zbMATH Keywords

quaternionexact order of approximation\(q\)-Bernstein operators of quaternionic variableanalytic functions in Weierstrass senseVoronovskaja-type results on disks

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Approximation in the complex plane (30E10) Rate of convergence, degree of approximation (41A25)

Related Items (4)

Overconvergence of Chebyshev and Legendre expansions in quaternionic ellipsoids ⋮ Pointwise approximation by Bernstein type operators in mobile interval ⋮ Approximation by quaternion \((p,q)\)-Bernstein polynomials and Voronovskaja type result on compact disk ⋮ Approximation of analytic functions by generalized Favard-Szász-Mirakjan-Faber operators in compact sets

Cites Work

• Unnamed Item
• Power series and analyticity over the quaternions
• \(q\)-Bernstein polynomials and their iterates.
• Die Funktionentheorie der Differentialgleichungen \(\Delta u=0\) und \(\Delta\Delta u=0\) mit vier reellen Variablen
• Saturation of convergence for \(q\)-Bernstein polynomials in the case \(q\geqslant 1\)
• Voronovskaja's theorem and iterations for complex Bernstein polynomials in compact disks
• A new theory of regular functions of a quaternionic variable
• Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen

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