Kantorovich-Bernstein polynomials

DOI10.1007/BF01888273zbMath0743.41022MaRDI QIDQ1814079

Z. Ditzian, Xin-Long Zhou

Publication date: 25 June 1992

Published in: Constructive Approximation (Search for Journal in Brave)

zbMATH Keywords

Kantorovich-Bernstein Polynomials

Mathematics Subject Classification ID

Approximation by positive operators (41A36) Inverse theorems in approximation theory (41A27) Saturation in approximation theory (41A40)

Related Items

The lower estimate for linear positive operators. II ⋮ The lower estimate for linear positive operators. I ⋮ The strong converse inequality for Bernstein-Kantorovich operators ⋮ Weighted \(L_ p\)-approximation of derivatives by the method of gammaoperators ⋮ Weighted approximation of functions in \(L_p\)-norm by Baskakov-Kantorovich operator ⋮ On linear combinations of multivariate generalized sampling type series ⋮ Weak type inequalities for best simultaneous approximation in Banach spaces ⋮ Asymptotic formulae for multivariate Kantorovich type generalized sampling series ⋮ Strong converse inequalities ⋮ Approximation by Means of Kantorovich-Stancu Type Operators ⋮ Strong converse inequality for Kantorovich polynomials ⋮ Quantitative Voronovskaya type results for a sequence of Stancu type operators

Cites Work

• Converse theorems for approximation by Bernstein polynomials in \(L_ p[0,1\) \((1<p<\infty)\)]
• Steckin-Marchaud-type inequalities in connection with Bernstein polynomials
• A global inverse theorem for combinations of Bernstein polynomials
• On interpolation of L//p[a,b and weighted Sobolev spaces]
• An interpolation theorem and its applications to positive operators
• The \(L^p\)-saturation of the Bernstein-Kantorovitch polynomials
• The \(L_1\) saturation class of the Kantorovic operator
• Sharp converse theorem of \(L^ p\)-polynomial approximation
• The approximation of continuous functions by positive linear operators
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