Approximation Properties of p,q-Szász-Mirakjan-Durrmeyer Operators
In this article, we introduce a new Durrmeyer-type generalization of p,q-Szász-Mirakjan operators using the p,q-gamma function of the second kind. The moments and central moments are obtained. Then, the Voronovskaja-type asymptotic formula is investigated and point-wise estimates of these operators...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6649570 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558285856702464 |
|---|---|
| author | Zhi-Peng Lin Wen-Tao Cheng Xiao-Wei Xu |
| author_facet | Zhi-Peng Lin Wen-Tao Cheng Xiao-Wei Xu |
| author_sort | Zhi-Peng Lin |
| collection | DOAJ |
| description | In this article, we introduce a new Durrmeyer-type generalization of p,q-Szász-Mirakjan operators using the p,q-gamma function of the second kind. The moments and central moments are obtained. Then, the Voronovskaja-type asymptotic formula is investigated and point-wise estimates of these operators are studied. Also, some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K-functional. Finally, the rate of convergence and weighted approximation of these operators are presented. |
| format | Article |
| id | doaj-art-fc49fa927cb94282a117c421989be214 |
| 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-fc49fa927cb94282a117c421989be2142025-02-03T01:32:53ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/66495706649570Approximation Properties of p,q-Szász-Mirakjan-Durrmeyer OperatorsZhi-Peng Lin0Wen-Tao Cheng1Xiao-Wei Xu2School of Information Science and Technology, Xiamen University Tan Kah Kee College, Fujian, Zhangzhou 363105, ChinaSchool of Mathematics and Physics, Anqing Normal University, Anhui, Anqing 246133, ChinaSchool of Computer and Data Engineering, NingboTech University, Zhejiang, Ningbo 315100, ChinaIn this article, we introduce a new Durrmeyer-type generalization of p,q-Szász-Mirakjan operators using the p,q-gamma function of the second kind. The moments and central moments are obtained. Then, the Voronovskaja-type asymptotic formula is investigated and point-wise estimates of these operators are studied. Also, some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K-functional. Finally, the rate of convergence and weighted approximation of these operators are presented.http://dx.doi.org/10.1155/2021/6649570 |
| spellingShingle | Zhi-Peng Lin Wen-Tao Cheng Xiao-Wei Xu Approximation Properties of p,q-Szász-Mirakjan-Durrmeyer Operators Journal of Function Spaces |
| title | Approximation Properties of p,q-Szász-Mirakjan-Durrmeyer Operators |
| title_full | Approximation Properties of p,q-Szász-Mirakjan-Durrmeyer Operators |
| title_fullStr | Approximation Properties of p,q-Szász-Mirakjan-Durrmeyer Operators |
| title_full_unstemmed | Approximation Properties of p,q-Szász-Mirakjan-Durrmeyer Operators |
| title_short | Approximation Properties of p,q-Szász-Mirakjan-Durrmeyer Operators |
| title_sort | approximation properties of p q szasz mirakjan durrmeyer operators |
| url | http://dx.doi.org/10.1155/2021/6649570 |
| work_keys_str_mv | AT zhipenglin approximationpropertiesofpqszaszmirakjandurrmeyeroperators AT wentaocheng approximationpropertiesofpqszaszmirakjandurrmeyeroperators AT xiaoweixu approximationpropertiesofpqszaszmirakjandurrmeyeroperators |