Approximation properties and error estimation of q-Bernstein shifted operators

In the present paper, q -analogue of Lupaş Bernstein operators with shifted knots are introduced. First, some basic results for convergence of the introduced operators are established and then the rate of convergence by these operators in terms of the modulus of continuity are obtained. Further, a V...

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Bibliographic Details
Published in:Numerical algorithms Vol. 84; no. 1; pp. 207 - 227
Main Authors: Mursaleen, Mohammad, Ansari, Khursheed J., Khan, Asif
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2020
Springer Nature B.V
Subjects:
Algebra
Algorithms
Approximation
Basic converters
Calculus
Computer Science
Convergence
Error analysis
Mathematical analysis
Numeric Computing
Numerical Analysis
Operators (mathematics)
Original Paper
Theory of Computation
Lupaş
Voronovskaja type theorem
functional
41A25
41A36
41A10
Local approximation
Bernstein shifted operators
Rate of convergence
Modulus of continuity
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In the present paper, q -analogue of Lupaş Bernstein operators with shifted knots are introduced. First, some basic results for convergence of the introduced operators are established and then the rate of convergence by these operators in terms of the modulus of continuity are obtained. Further, a Voronovskaja type theorem and local approximation results for the said operators are studied. Error estimation tables are presented with respect to different parameters. We also show comparisons by some illustrative graphics for the convergence of operators to a function with the help of MATLAB R2018a.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-019-00752-4