Genuine Bernstein-Durrmeyer type operators preserving 1 and \(x^j\)

DOI10.1007/S43034-023-00305-WMaRDI QIDQ6144628

Ulrich Abel, Ioan Raşa, Ana-Maria Acu, Margareta Heilmann

Publication date: 8 January 2024

Published in: Annals of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

generalized convex functionVoronovskaya-type formulasgenuine Bernstein-Durrmeyer operatorAldaz-Kounchev-Render operator

Mathematics Subject Classification ID

Convexity of real functions in one variable, generalizations (26A51) Approximation by positive operators (41A36)

Cites Work

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• Asymptotic formulae via a Korovkin-type result
• Bernstein-type operators which preserve polynomials
• Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces
• General King-type operators
• Shape preserving approximation by Bernstein-type operators which fix polynomials
• 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
• The Bernstein Voronovskaja-type theorem for positive linear approximation operators
• Ohlin's lemma and some inequalities of the Hermite-Hadamard type
• Hadamard-type inequalities for generalized convex functions
• Another look at Voronovskaja type formulas
• A Quantitative Variant of Voronovskaja's Theorem for King-Type Operators
• On the composition and decomposition of positive linear operators (VII)

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