Generalized Popoviciu expansions for Bernstein polynomials of a rational module

DOI10.1007/s10958-022-05948-zOpenAlexW4283011322MaRDI QIDQ2160254

V. B. Sherstyukov, I. V. Tikhonov, D. G. Tsvetkovich

Publication date: 3 August 2022

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-022-05948-z

zbMATH Keywords

Bernstein polynomialpiecewise linear functionrational moduledomain of convergencedistribution of zeros of polynomialgeneralized Popoviciu expansionKantorovich lemniscate

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)

Related Items (1)

On a connection of Bernstein and Kantorovich polynomials for a symmetric modulus function

Cites Work

• Deficient Bernstein polynomials
• Rate of convergence of Bernstein polynomials for functions with derivatives of bounded variation
• Inequalities for binomial coefficients
• On the sharpness of Jentzsch-Szegö-type theorems
• Closed form summation for classical distributions: variations on a theme of de Moivre
• Asymptotics of the roots of Bernstein polynomials used in the construction of modified Daubechies wavelets.
• Interpolation and approximation by polynomials
• Stieltjes integral representation of convex functions
• Gluing Rule for Bernstein Polynomials on the Symmetric Interval
• Bernstein Operators and Their Properties
• The Binomial Coefficient Function
• Bernstein Polynomials for a Standard Module Function on the Symmetric Interval
• On the Theorem of Jentzsch
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