On statistical approximation properties of Kantorovich type \(q\)-Bernstein operators

DOI10.1016/j.mcm.2010.05.005zbMath1202.41017OpenAlexW1526939662MaRDI QIDQ614304

Ogün Doğru, Özge Dalmanoğlu

Publication date: 27 December 2010

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2010.05.005

zbMATH Keywords

modulus of continuitystatistical convergence\(q\)-integersKorovkin theoremKantorovich type operatorsLipschitz class

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Approximation by operators (in particular, by integral operators) (41A35) Ideal and statistical convergence (40A35)

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Shape-preserving properties of a new family of generalized Bernstein operators, Bernstein-Schurer-Kantorovich operators based on \(q\)-integers, Stancu type generalization of \(q\)-Favard-Szàsz operators, Some statistical approximation properties of Kantorovich-type \(q\)-Bernstein-Stancu operators, Statistical approximation of modified Schurer-type \(q\)-Bernstein Kantorovich operators, On statistical approximation properties of the Kantorovich type Lupaş operators, Approximation properties of Kantorovich type \(q\)-Balázs-Szabados operators, GBS operators of Bernstein-Schurer-Kantorovich type based on \(q\)-integers, Statistical approximation properties of \(\lambda\)-Bernstein operators based on \(q\)-integers, Rate of Convergence of Modified Schurer-Type q-Bernstein Kantorovich Operators, Statistical Approximation of the q-Bernstein-Durrmeyer Type Operators, Extended Bernstein-Kantorovich-Stancu Operators with Multiple Parameters and Approximation Properties, Statistical approximation of \(q\)-Bernstein-Scourer-Stancu-Kantorovich operators

Cites Work

• Convergence of generalized Bernstein polynomials
• Voronovskaya-type formulas and saturation of convergence for \(q\)-Bernstein polynomials for \(0 < q < 1\)
• On approximation by a class of new Bernstein type operators
• Statistical approximation results for Kantorovich-type operators involving some special polynomials
• On certain \(q\)-Durrmeyer type operators
• Sur l'approximation de fonctions intégrables sur l'interval-0,1-ferme par des polynômes de Bernstein modifies
• Korovkin-type approximation theory and its applications
• \(q\)-Bernstein polynomials and their iterates.
• Some approximation theorems via statistical convergence.
• Integral inequalities in \(q\)-calculus
• The inequalities for some types of \(q\)-integrals
• On the Lupaş \(q\)-analogue of the Bernstein operator
• Some approximation properties of \(q\)-Durrmeyer operators
• The rate of convergence ofq-Durrmeyer operators for 0<q<1
• On integral type generalizations of positive linear operators
• Sur la convergence statistique
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