Approximation Theorem for New Modification of q-Bernstein Operators on (0,1)
In this work, we extend the works of F. Usta and construct new modified q-Bernstein operators using the second central moment of the q-Bernstein operators defined by G. M. Phillips. The moments and central moment computation formulas and their quantitative properties are discussed. Also, the Korovki...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6694032 |
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| author | Yun-Shun Wu Wen-Tao Cheng Feng-Lin Chen Yong-Hui Zhou |
| author_facet | Yun-Shun Wu Wen-Tao Cheng Feng-Lin Chen Yong-Hui Zhou |
| author_sort | Yun-Shun Wu |
| collection | DOAJ |
| description | In this work, we extend the works of F. Usta and construct new modified q-Bernstein operators using the second central moment of the q-Bernstein operators defined by G. M. Phillips. The moments and central moment computation formulas and their quantitative properties are discussed. Also, the Korovkin-type approximation theorem of these operators and the Voronovskaja-type asymptotic formula are investigated. Then, two local approximation theorems using Peetre’s K-functional and Steklov mean and in terms of modulus of smoothness are obtained. Finally, the rate of convergence by means of modulus of continuity and three different Lipschitz classes for these operators are studied, and some graphs and numerical examples are shown by using Matlab algorithms. |
| format | Article |
| id | doaj-art-bbbbfa3c46dd4061903e0a95bb66bd7c |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-bbbbfa3c46dd4061903e0a95bb66bd7c2025-02-03T07:23:53ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/66940326694032Approximation Theorem for New Modification of q-Bernstein Operators on (0,1)Yun-Shun Wu0Wen-Tao Cheng1Feng-Lin Chen2Yong-Hui Zhou3School of Mathematical Sciences, Guizhou Normal University, Guizhou, Guiyang 550001, ChinaSchool of Mathematics and Physics, Anqing Normal University, Anhui, Anqing 246133, ChinaSchool of Mathematics and Physics, Anqing Normal University, Anhui, Anqing 246133, ChinaSchool of Big Data and Computer Science, Guizhou Normal University, Guizhou, Guiyang 550001, ChinaIn this work, we extend the works of F. Usta and construct new modified q-Bernstein operators using the second central moment of the q-Bernstein operators defined by G. M. Phillips. The moments and central moment computation formulas and their quantitative properties are discussed. Also, the Korovkin-type approximation theorem of these operators and the Voronovskaja-type asymptotic formula are investigated. Then, two local approximation theorems using Peetre’s K-functional and Steklov mean and in terms of modulus of smoothness are obtained. Finally, the rate of convergence by means of modulus of continuity and three different Lipschitz classes for these operators are studied, and some graphs and numerical examples are shown by using Matlab algorithms.http://dx.doi.org/10.1155/2021/6694032 |
| spellingShingle | Yun-Shun Wu Wen-Tao Cheng Feng-Lin Chen Yong-Hui Zhou Approximation Theorem for New Modification of q-Bernstein Operators on (0,1) Journal of Function Spaces |
| title | Approximation Theorem for New Modification of q-Bernstein Operators on (0,1) |
| title_full | Approximation Theorem for New Modification of q-Bernstein Operators on (0,1) |
| title_fullStr | Approximation Theorem for New Modification of q-Bernstein Operators on (0,1) |
| title_full_unstemmed | Approximation Theorem for New Modification of q-Bernstein Operators on (0,1) |
| title_short | Approximation Theorem for New Modification of q-Bernstein Operators on (0,1) |
| title_sort | approximation theorem for new modification of q bernstein operators on 0 1 |
| url | http://dx.doi.org/10.1155/2021/6694032 |
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