Applications of Generalized Weighted Statistical Convergence to Approximation Theorems for Functions of One and Two Variables

DOI10.1080/01630563.2020.1868503zbMath1472.40003OpenAlexW3125141683MaRDI QIDQ4985171

Faruk Özger

Publication date: 22 April 2021

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2020.1868503

zbMATH Keywords

\(\lambda\)-Bernstein operatorsbivariate Bernstein operatorsrate of weighted statistical convergencestatistical approximation propertiesweighted statistical Voronovskaja-type theorem

Mathematics Subject Classification ID

Rate of convergence, degree of approximation (41A25) Approximation by positive operators (41A36) Ideal and statistical convergence (40A35)

Related Items (9)

On a Stancu form Szász-Mirakjan-Kantorovich operators based on shape parameter \(\lambda\) ⋮ Numerical and theoretical approximation results for Schurer-Stancu operators with shape parameter \(\lambda\) ⋮ Some approximation results on a class of new type λ-Bernstein polynomials ⋮ Statistical weighted \((N_\lambda,p,q)(E_\lambda,1)\) \(A\)-summability with application to Korovkin's type approximation theorem ⋮ Generalized blending type Bernstein operators based on the shape parameter \(\lambda\) ⋮ On the Durrmeyer variant of \(q\)-Bernstein operators based on the shape parameter \(\lambda\) ⋮ Some new inequalities and numerical results of bivariate Bernstein-type operator including Bézier basis and its GBS operator ⋮ Unnamed Item ⋮ A numerical comparative study of generalized Bernstein-Kantorovich operators

Cites Work

• Statistical weighted \(A\)-summability with application to Korovkin's type approximation theorem
• Weighted statistical convergence and its application to Korovkin type approximation theorem
• Approximation properties of \(\lambda\)-Bernstein operators
• The Bézier variant of Kantorovich type \(\lambda\)-Bernstein operators
• Approximation properties of \(\lambda\)-Kantorovich operators
• Blending type approximation by \(GBS\) operators of bivariate tensor product of \(\lambda\)-Bernstein-Kantorovich type
• Some approximation theorems via statistical convergence.
• The approximation properties of generalized Bernstein polynomials of two variables
• Approximation of functions by a new class of generalized Bernstein-Schurer operators
• Approximation on parametric extension of Baskakov-Durrmeyer operators on weighted spaces
• Approximation of functions by Stancu variant of Bernstein-Kantorovich operators based on shape parameter \(\alpha\)
• Construction of Stancu-type Bernstein operators based on Bézier bases with shape parameter \(\lambda\)
• Approximation of functions by a class of Durrmeyer-Stancu type operators which includes Euler's beta function
• Approximation by Kantorovich Variant of λ—Schurer Operators and Related Numerical Results
• On new Bézier bases with Schurer polynomials and corresponding results in approximation theory
• Local approximation properties for certain King type operators
• Sur la convergence statistique
• Weighted statistical approximation properties of univariate and bivariate λ-Kantorovich operators
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