A numerical comparative study of generalized Bernstein-Kantorovich operators
type: Item
instance of: scholarly article
title: A numerical comparative study of generalized Bernstein-Kantorovich operators
zbMATH Open document ID: 1491.41003
author: Uğur Kadak
author: Faruk Özger
published in: Mathematical Foundations of Computing
publication date: 2022-01-11T00:00:00Z
review text: A generalization of the Bernstein-Kantorovich operators involving multiple shape parameters is introduced, establishing Voronovskaja and Grüss-Voronovskaja type theorems, the statistical convergence and the statistical rate of convergence obtained by means of a regular summability matrix. The new operators are compared with the classical Bernstein, Bernstein-Kantorovich, \(\lambda\)-Bernstein, \(\lambda\)-Bernstein-Kantorovich, \(\alpha\)-Bernstein and \(\alpha\)-Bernstein-Kantorovich operators, respectively.
reviewed by: Zoltán Finta
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 26A16
Mathematics Subject Classification ID: 40C05
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 7455694
zbMATH Keywords: multiple shape parameter
zbMATH Keywords: infinite matrices
zbMATH Keywords: Lipschitz continuous function
zbMATH Keywords: Voronovskaja asymptotic formula
zbMATH Keywords: Maple algorithm
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: mfc.2021021
OpenAlex ID: W3203673439
cites work: Approximation properties of \(\lambda\)-Kantorovich operators
cites work: Approximation of functions by a class of Durrmeyer-Stancu type operators which includes Euler's beta function
cites work: On approximation of continuous and of analytic functions
cites work: The Bézier variant of Kantorovich type \(\lambda\)-Bernstein operators
cites work: Approximation properties of \(\lambda\)-Bernstein operators
cites work: Approximation of functions by a new family of generalized Bernstein operators
cites work: Korovkin type approximation theorems inb-statistical sense
cites work: Q3817079
cites work: Q4273944
cites work: Statistical approximation by positive linear operators
cites work: An alternative distribution function estimation method using rational Bernstein polynomials
cites work: Remark on Voronovskaja theorem for \(q\)--Bernstein operators
cites work: Some approximation theorems via statistical convergence.
cites work: Gr\"uss and Gr\"uss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables
cites work: A novel generalization of Bézier curve and surface
cites work: Continuity conditions for Q-Bézier curves of degree \(n\)
cites work: Convergence of generalized Bernstein polynomials
cites work: On relative weighted summability in modular function spaces and associated approximation theorems
cites work: Chlodowsky type generalization of \((p,q)\)-Szász operators involving Brenke type polynomials
cites work: A new approach to improve the order of approximation of the Bernstein operators: theory and applications
cites work: Q5818792
cites work: Generalized weighted invariant mean based on fractional difference operator with applications to approximation theorems for functions of two variables
cites work: Modularly weighted four dimensional matrix summability with application to Korovkin type approximation theorem
cites work: Statistical weighted \(\mathcal{B}\)-summability and its applications to approximation theorems
cites work: Extended Bernstein-Kantorovich-Stancu Operators with Multiple Parameters and Approximation Properties
cites work: Some approximation results for Stancu type Lupaş-Schurer operators based on \((p, q)\)-integers
cites work: Blending‐type approximation by Lupaş–Durrmeyer‐type operators involving Pólya distribution
cites work: Multidimensional Bernstein polynomials and Bézier curves: analysis of machine learning algorithm for facial expression recognition based on curvature
cites work: Approximation of functions by Stancu variant of Bernstein-Kantorovich operators based on shape parameter \(\alpha\)
cites work: Approximation by bivariate generalized Bernstein-Schurer operators and associated GBS operators
cites work: Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems
cites work: Construction of a new family of Bernstein-Kantorovich operators
cites work: Local approximation properties for certain King type operators
cites work: Weighted statistical approximation properties of univariate and bivariate λ-Kantorovich operators
cites work: Approximation by Kantorovich Variant of λ—Schurer Operators and Related Numerical Results
cites work: On new Bézier bases with Schurer polynomials and corresponding results in approximation theory
cites work: Applications of Generalized Weighted Statistical Convergence to Approximation Theorems for Functions of One and Two Variables
cites work: Approximation of functions by a new class of generalized Bernstein-Schurer operators
cites work: Construction of Stancu-type Bernstein operators based on Bézier bases with shape parameter \(\lambda\)
cites work: Bernstein polynomial basis for numerical solution of boundary value problems
cites work: Expansion of moments of Bernstein polynomials
DOI: 10.3934/MFC.2021021
description: scientific article; zbMATH DE number 7455694