On the monotonicity property for the sequence of classical Bernstein operators

DOI10.1007/s13370-018-0602-4zbMath1413.41031OpenAlexW2883299391WikidataQ129529714 ScholiaQ129529714MaRDI QIDQ1715768

Dan Miclăuş

Publication date: 29 January 2019

Published in: Afrika Matematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13370-018-0602-4

zbMATH Keywords

monotonicityBernstein operatorconvex functionremainder termdivided differencePopoviciu theorem

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Convexity of real functions in one variable, generalizations (26A51) Approximation by positive operators (41A36) Remainders in approximation formulas (41A80)

Cites Work

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• Composite Bernstein cubature
• Bernstein collocation method for solving nonlinear differential equations
• Properties and applications of \(P_n\)-simple functionals
• The generalization of the Bernstein operator on any finite interval
• On the monotonicity of the sequence formed by the first order derivatives of the Bernstein polynomials
• Stieltjes integral representation of convex functions

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