On Durrmeyer Type λ-Bernstein Operators via (p, q)-Calculus
In the present paper, Durrmeyer type λ-Bernstein operators via (p, q)-calculus are constructed, the first and second moments and central moments of these operators are estimated, a Korovkin type approximation theorem is established, and the estimates on the rate of convergence by using the modulus o...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/8832627 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561182116937728 |
|---|---|
| author | Qing-Bo Cai Guorong Zhou |
| author_facet | Qing-Bo Cai Guorong Zhou |
| author_sort | Qing-Bo Cai |
| collection | DOAJ |
| description | In the present paper, Durrmeyer type λ-Bernstein operators via (p, q)-calculus are constructed, the first and second moments and central moments of these operators are estimated, a Korovkin type approximation theorem is established, and the estimates on the rate of convergence by using the modulus of continuity of second order and Steklov mean are studied, a convergence theorem for the Lipschitz continuous functions is also obtained. Finally, some numerical examples are given to show that these operators we defined converge faster in some λ cases than Durrmeyer type (p, q)-Bernstein operators. |
| format | Article |
| id | doaj-art-e34582ad939f47619f12fbd654c45074 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e34582ad939f47619f12fbd654c450742025-02-03T01:25:47ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/88326278832627On Durrmeyer Type λ-Bernstein Operators via (p, q)-CalculusQing-Bo Cai0Guorong Zhou1School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, ChinaSchool of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaIn the present paper, Durrmeyer type λ-Bernstein operators via (p, q)-calculus are constructed, the first and second moments and central moments of these operators are estimated, a Korovkin type approximation theorem is established, and the estimates on the rate of convergence by using the modulus of continuity of second order and Steklov mean are studied, a convergence theorem for the Lipschitz continuous functions is also obtained. Finally, some numerical examples are given to show that these operators we defined converge faster in some λ cases than Durrmeyer type (p, q)-Bernstein operators.http://dx.doi.org/10.1155/2020/8832627 |
| spellingShingle | Qing-Bo Cai Guorong Zhou On Durrmeyer Type λ-Bernstein Operators via (p, q)-Calculus Journal of Function Spaces |
| title | On Durrmeyer Type λ-Bernstein Operators via (p, q)-Calculus |
| title_full | On Durrmeyer Type λ-Bernstein Operators via (p, q)-Calculus |
| title_fullStr | On Durrmeyer Type λ-Bernstein Operators via (p, q)-Calculus |
| title_full_unstemmed | On Durrmeyer Type λ-Bernstein Operators via (p, q)-Calculus |
| title_short | On Durrmeyer Type λ-Bernstein Operators via (p, q)-Calculus |
| title_sort | on durrmeyer type λ bernstein operators via p q calculus |
| url | http://dx.doi.org/10.1155/2020/8832627 |
| work_keys_str_mv | AT qingbocai ondurrmeyertypelbernsteinoperatorsviapqcalculus AT guorongzhou ondurrmeyertypelbernsteinoperatorsviapqcalculus |