An answer to an open problem on the multivariate Bernstein polynomials on a simplex

DOI10.1007/s00025-018-0938-yzbMath1411.41010OpenAlexW2905401335WikidataQ128811376 ScholiaQ128811376MaRDI QIDQ1729893

Ioan Gavrea, Mircea Ivan

Publication date: 28 February 2019

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-018-0938-y

zbMATH Keywords

convexitysimplexmultivariate Bernstein polynomials

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by positive operators (41A36)

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Cites Work

• On a conjecture concerning the sum of the squared Bernstein polynomials
• Complete monotonicity and zeros of sums of squared Baskakov functions
• Inequalities for ultraspherical polynomials. Proof of a conjecture of I. Raşa
• Korovkin-type approximation theory and its applications
• On a new sequence of positive linear operators related to squared Bernstein polynomials
• Convexity properties of some entropies
• Chebyshev-Gr\"{u}ss-type inequalities via discrete oscillations