Construction of Stancu-Type Bernstein Operators Based on Bézier Bases with Shape Parameter λ
Date
2019
Authors
Srivastava, H. M.
Özger, Faruk
Mohiuddine, S.A.
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter λ∈[−1,1] and calculate their moments. The uniform convergence of the operator and global approximation result by means of Ditzian-Totik modulus of smoothness are established. Also, we establish the direct approximation theorem with the help of second order modulus of smoothness, calculate the rate of convergence via Lipschitz-type function, and discuss the Voronovskaja-type approximation theorems. Finally, in the last section, we construct the bivariate case of Stancu-type λ -Bernstein operators and study their approximation behaviors.
Description
Keywords
Stancu-type Bernstein operators, B�zier bases, Voronovskaja-type theorems, modulus of continuity, rate of convergence, bivariate operators, approximation properties
Citation
Srivastava, H.M., Özger, F. & Mohiuddine, S.A. (2019). Construction of Stancu-Type Bernstein Operators Based on Bézier Bases with Shape Parameter λ. Symmetry, 11(3), 316. https://doi.org/10.3390/sym11030316