On Pointwise Convergence ofq-Bernstein Operators and Theirq-Derivatives

DOI10.1080/01630563.2014.970646zbMath1312.41021OpenAlexW2035041627MaRDI QIDQ5251588

Ali Aral, Tuncer Acar

Publication date: 20 May 2015

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

Full work available at URL: https://doi.org/10.1080/01630563.2014.970646

zbMATH Keywords

\(q\)-derivative\(q\)-Bernstein operatorsquantitative Voronovskaya-type theorem

Mathematics Subject Classification ID

Rate of convergence, degree of approximation (41A25) Approximation by positive operators (41A36)

Related Items (32)

On Kantorovich modification of \((p,q) \)-Baskakov operators ⋮ Blending type approximation by q‐generalized Boolean sum of Durrmeyer type ⋮ Some approximation properties of \((p,q)\)-Bernstein operators ⋮ Quantitative \(q\)-Voronovskaya and \(q\)-Grüss-Voronovskaya-type results for \(q\)-Szász operators ⋮ q-Voronovskaya type theorems forq-Baskakov operators ⋮ Approximation by modified Szász-Durrmeyer operators ⋮ Asymptotic formulas for generalized Szász-Mirakyan operators ⋮ Bivariate tensor product \((p, q)\)-analogue of Kantorovich-type Bernstein-Stancu-Schurer operators ⋮ Iterates of \(q\)-Bernstein operators on triangular domain with all curved sides ⋮ Rate of convergence of Stancu type modified \(q\)-Gamma operators for functions with derivatives of bounded variation ⋮ Approximation results on Dunkl generalization of Phillips operators via \(q\)-calculus ⋮ Some bivariate Durrmeyer operators based on q-integers ⋮ Approximation by modified q‐Gamma type operators in a polynomial weighted space ⋮ Approximation by α$$ \alpha $$‐Bernstein–Schurer operators and shape preserving properties via q$$ q $$‐analogue ⋮ Voronovskaya Type Theorems in Weighted Spaces ⋮ Evaluation of norm of \((p,q)\)-Bernstein operators ⋮ Approximation properties of \(\lambda\)-Gamma operators based on \(q\)-integers ⋮ Approximation theorem for new modification of \(q\)-Bernstein operators on (0,1) ⋮ On Durrmeyer-type generalization of \((p,q)\)-Bernstein operators ⋮ Phillips-type \(q\)-Bernstein operators on triangles ⋮ Quantum Lorentz degrees of polynomials and a Pólya theorem for polynomials positive on \(q\)-lattices ⋮ Approximation by bivariate \((p,q)\)-Bernstein-Kantorovich operators ⋮ On Kantorovich modification of \((p,q)\)-Bernstein operators ⋮ On approximation to discrete \(q\)-derivatives of functions via \(q\)-Bernstein-Schurer operators ⋮ Approximation on a class of Phillips operators generated by \(q\)-analogue ⋮ Approximation properties of certain Bernstein-Stancu type operators ⋮ Construction of Stancu-type Bernstein operators based on Bézier bases with shape parameter \(\lambda\) ⋮ Some approximation properties of a Durrmeyer variant of q‐Bernstein–Schurer operators ⋮ Generalized Bernstein-Durrmeyer operators of blending type ⋮ The new forms of Voronovskaya's theorem in weighted spaces ⋮ Dunkl generalization of Szász operators via \(q\)-calculus ⋮ A basic problem of \((p,q)\)-Bernstein-type operators

Cites Work

• A generalization of Szász-Mirakyan operators based on \(q\)-integers
• The moments for \(q\)-Bernstein operators in the case \(0<q<1\)
• Bernstein-Type Operators on the Half Line
• Applications of q-Calculus in Operator Theory

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