The Bézier variant of Kantorovich type \(\lambda\)-Bernstein operators

DOI10.1186/s13660-018-1688-9zbMath1497.41012OpenAlexW2800107547WikidataQ55420966 ScholiaQ55420966MaRDI QIDQ824533

Qing-Bo Cai

Publication date: 15 December 2021

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-018-1688-9

zbMATH Keywords

rate of convergencemodulus of continuitybasis functionsabsolutely continuous functions\(\lambda\)-Bernstein operators

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Approximation by operators (in particular, by integral operators) (41A35) Approximation by positive operators (41A36)

Related Items (20)

Blending type approximation by \(GBS\) operators of bivariate tensor product of \(\lambda\)-Bernstein-Kantorovich type ⋮ Approximation by bivariate generalized Bernstein-Schurer operators and associated GBS operators ⋮ Numerical and theoretical approximation results for Schurer-Stancu operators with shape parameter \(\lambda\) ⋮ Approximation of functions by a class of Durrmeyer-Stancu type operators which includes Euler's beta function ⋮ Generalized blending type Bernstein operators based on the shape parameter \(\lambda\) ⋮ On the shape-preserving properties of \(\lambda\)-Bernstein operators ⋮ λ-Bernstein Operators Based on Pólya Distribution ⋮ Approximation process based on parametric generalization of Schurer-Kantorovich operators and their bivariate form ⋮ The family of \(\lambda\)-Bernstein-Durrmeyer operators based on certain parameters ⋮ Approximation by α$$ \alpha $$‐Bernstein–Schurer operators and shape preserving properties via q$$ q $$‐analogue ⋮ Approximation of functions by a new class of generalized Bernstein-Schurer operators ⋮ Approximation by one and two variables of the Bernstein-Schurer-type operators and associated GBS operators on symmetrical mobile interval ⋮ Approximation properties of generalized \(\lambda\)-Bernstein-Stancu-type operators ⋮ Convergence of \(\lambda\)-Bernstein operators via power series summability method ⋮ A numerical comparative study of generalized Bernstein-Kantorovich operators ⋮ Applications of Generalized Weighted Statistical Convergence to Approximation Theorems for Functions of One and Two Variables ⋮ Approximation properties of \(\lambda\)-Bernstein-Kantorovich-Stancu operators ⋮ Extended Bernstein-Kantorovich-Stancu Operators with Multiple Parameters and Approximation Properties ⋮ Construction of Stancu-type Bernstein operators based on Bézier bases with shape parameter \(\lambda\) ⋮ Weighted statistical approximation properties of univariate and bivariate λ-Kantorovich operators

Cites Work

• Approximation by Kantorovich type \(q\)-Bernstein-Stancu operators
• Bernstein-type operators and their derivatives
• On \((p, q)\)-analogue of Bernstein operators
• Approximation properties of \(\lambda\)-Bernstein operators
• Rate of convergence of Bernstein polynomials for functions with derivatives of bounded variation
• On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions
• Pointwise approximation for linear combinations of Bernstein operators
• Some approximation results by \((p, q)\)-analogue of Bernstein-Stancu operators
• On \(q\)-analogue of Bernstein-Schurer-Stancu operators
• Some approximation properties of \(q\)-Durrmeyer operators
• Approximation properties for generalized \(q\)-Bernstein polynomials
• On the rates of approximation of Bernstein type operators.
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