Statistical approximation properties of λ-Bernstein operators based on q-integers
In this paper, we introduce a new generalization of λ-Bernstein operators based on q-integers, we obtain the moments and central moments of these operators, establish a statistical approximation theorem and give an example to show the convergence of these operators to f(x). It can be seen that in so...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-05-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2019-0039 |
| _version_ | 1818737089675526144 |
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| author | Cai Qing-Bo Zhou Guorong Li Junjie |
| author_facet | Cai Qing-Bo Zhou Guorong Li Junjie |
| author_sort | Cai Qing-Bo |
| collection | DOAJ |
| description | In this paper, we introduce a new generalization of λ-Bernstein operators based on q-integers, we obtain the moments and central moments of these operators, establish a statistical approximation theorem and give an example to show the convergence of these operators to f(x). It can be seen that in some cases the absolute error bounds are smaller than the case of classical q-Bernstein operators to f(x). |
| first_indexed | 2024-12-18T00:47:30Z |
| format | Article |
| id | doaj.art-51f55592a3bd4ac3956f7a0811c07c95 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-18T00:47:30Z |
| publishDate | 2019-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-51f55592a3bd4ac3956f7a0811c07c952022-12-21T21:26:45ZengDe GruyterOpen Mathematics2391-54552019-05-0117148749810.1515/math-2019-0039math-2019-0039Statistical approximation properties of λ-Bernstein operators based on q-integersCai Qing-Bo0Zhou Guorong1Li Junjie2School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, 362000, ChinaSchool of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, ChinaSchool of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, ChinaIn this paper, we introduce a new generalization of λ-Bernstein operators based on q-integers, we obtain the moments and central moments of these operators, establish a statistical approximation theorem and give an example to show the convergence of these operators to f(x). It can be seen that in some cases the absolute error bounds are smaller than the case of classical q-Bernstein operators to f(x).https://doi.org/10.1515/math-2019-0039q-integersλ-bernstein operatorsstatistical convergencebasis function41a1041a2541a36 |
| spellingShingle | Cai Qing-Bo Zhou Guorong Li Junjie Statistical approximation properties of λ-Bernstein operators based on q-integers Open Mathematics q-integers λ-bernstein operators statistical convergence basis function 41a10 41a25 41a36 |
| title | Statistical approximation properties of λ-Bernstein operators based on q-integers |
| title_full | Statistical approximation properties of λ-Bernstein operators based on q-integers |
| title_fullStr | Statistical approximation properties of λ-Bernstein operators based on q-integers |
| title_full_unstemmed | Statistical approximation properties of λ-Bernstein operators based on q-integers |
| title_short | Statistical approximation properties of λ-Bernstein operators based on q-integers |
| title_sort | statistical approximation properties of λ bernstein operators based on q integers |
| topic | q-integers λ-bernstein operators statistical convergence basis function 41a10 41a25 41a36 |
| url | https://doi.org/10.1515/math-2019-0039 |
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