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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| Veröffentlicht in: | Advances in difference equations Jg. 2020; H. 1; S. 1 - 17 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. Abstract 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. |
| ArticleNumber | 676 |
| Author | Mohiuddine, S. A. |
| Author_xml | – sequence: 1 givenname: S. A. orcidid: 0000-0002-9050-9104 surname: Mohiuddine fullname: Mohiuddine, S. A. email: mohiuddine@gmail.com organization: Department of General Required Courses, Mathematics, Faculty of Applied Studies, King Abdulaziz University, Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University |
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| Cites_doi | 10.1186/s13660-018-1909-2 10.1007/978-3-662-02888-9 10.1007/s40995-020-00914-3 10.1007/s40995-020-01018-8 10.1017/S0004972700004494 10.1007/s13398-018-0591-z 10.1007/s00025-018-0838-1 10.1186/s13660-018-1653-7 10.1007/s40995-020-01024-w 10.1186/s13662-020-02925-1 10.2298/FIL1911473O 10.1007/s40995-016-0045-4 10.1186/s13660-016-1045-9 10.1007/s11785-016-0633-5 10.1007/978-1-4612-1360-4 10.1186/s13660-018-1688-9 10.1007/s00025-018-0773-1 10.1007/s13398-020-00802-w 10.1186/s13660-018-1693-z 10.1007/s11785-016-0572-1 10.3390/sym11030316 10.1007/s00025-018-0789-6 10.1186/s13660-019-2055-1 10.1080/01630563.2015.1056914 10.1016/j.jmaa.2016.12.075 10.2298/FIL1914549M 10.1080/03081079.2019.1608985 10.5269/bspm.v37i4.35852 10.1007/s40995-017-0433-4 10.1002/mma.4559 10.1007/s13398-020-00903-6 10.1002/mma.5762 10.1016/j.amc.2013.11.095 10.1515/crll.1934.170.197 10.1016/j.amc.2013.03.115 10.37193/CMI.2013.01.09 |
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| Keywords | Bernstein operators Bögel differentiable function 41A25 41A36 Bivariate GBS operators 41A10 Bernstein–Schurer operators Modulus of continuity |
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| Snippet | 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... 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... Abstract We construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate... |
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| SubjectTerms | 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 |
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| Title | Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators |
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