Direct and converse theorems for King type operators

DOI10.3934/mfc.2022015zbMath1528.41063OpenAlexW4285283882WikidataQ113692639 ScholiaQ113692639MaRDI QIDQ6167861

Zoltán Finta

Publication date: 7 August 2023

Published in: Mathematical Foundations of Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mfc.2022015

zbMATH Keywords

Bernstein operatorsKing type operatorsBerens-Lorentz lemmafirst order Ditzian-Totik modulus of smoothness

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Approximation by positive operators (41A36)

Cites Work

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• Asymptotic formulae via a Korovkin-type result
• Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces
• Local and global approximation theorems for positive linear operators
• Positive linear operators which preserve \(x^2\)
• Complete asymptotic expansions related to conjecture on a Voronovskaja-type theorem
• A proof of a conjecture about the asymptotic formula of a Bernstein type operator
• Direct and converse theorems for King operators
• On sequences of J. P. King-type operators
• New properties of King's operators
• Bernstein type operators having 1 and \(x^j\) as fixed points
• A Quantitative Variant of Voronovskaja's Theorem for King-Type Operators

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