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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Vydané v:Numerical algorithms Ročník 84; číslo 1; s. 207 - 227
Hlavní autori: Mursaleen, Mohammad, Ansari, Khursheed J., Khan, Asif
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.05.2020
Springer Nature B.V
Predmet:
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
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Abstract 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.
AbstractList 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.
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.
Author Khan, Asif
Mursaleen, Mohammad
Ansari, Khursheed J.
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  surname: Ansari
  fullname: Ansari, Khursheed J.
  organization: Department of Mathematics, College of Science, King Khalid University
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  givenname: Asif
  surname: Khan
  fullname: Khan, Asif
  organization: Department of Mathematics, Aligarh Muslim University
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Cites_doi 10.1016/j.aml.2010.07.004
10.1007/s40010-016-0267-z
10.1186/s13660-016-1045-9
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Issue 1
Keywords Lupaş
Voronovskaja type theorem
functional
41A25
41A36
41A10
Local approximation
Bernstein shifted operators
Rate of convergence
Modulus of continuity
Language English
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PublicationTitle Numerical algorithms
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Snippet In the present paper, q -analogue of Lupaş Bernstein operators with shifted knots are introduced. First, some basic results for convergence of the introduced...
In the present paper, q-analogue of Lupaş Bernstein operators with shifted knots are introduced. First, some basic results for convergence of the introduced...
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SubjectTerms Algebra
Algorithms
Approximation
Basic converters
Calculus
Computer Science
Convergence
Error analysis
Mathematical analysis
Numeric Computing
Numerical Analysis
Operators (mathematics)
Original Paper
Theory of Computation
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Title Approximation properties and error estimation of q-Bernstein shifted operators
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