Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators

We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K -functional of our newly defined operators. Moreover, we define the associated generalized B...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2020; no. 1; pp. 1 - 17
Main Author: Mohiuddine, S. A.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2020
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications
Approximation
Bivariate analysis
Bivariate α-Bernstein–Schurer operators
Boolean algebra
Bögel differentiable function
Difference and Functional Equations
Functional Analysis
GBS operators
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Modulus of continuity
Operators
Ordinary Differential Equations
Partial Differential Equations
Smoothness
Topics in Special Functions and q-Special Functions: Theory
α-Bernstein operators
Bernstein operators
Bögel differentiable function
41A25
41A36
Bivariate
GBS operators
41A10
Bernstein–Schurer operators
Modulus of continuity
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K -functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-03125-7