Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators
The objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defined. The convergence property of the Bernstein gene...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/10/537 |
| _version_ | 1797475365972606976 |
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| author | Seng Huat Ong Choung Min Ng Hong Keat Yap Hari Mohan Srivastava |
| author_facet | Seng Huat Ong Choung Min Ng Hong Keat Yap Hari Mohan Srivastava |
| author_sort | Seng Huat Ong |
| collection | DOAJ |
| description | The objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defined. The convergence property of the Bernstein generalization is established. It is also shown that the Cheney–Sharma operator is the Szász–Mirakyan operator averaged by a certain probability distribution. |
| first_indexed | 2024-03-09T20:43:08Z |
| format | Article |
| id | doaj.art-cb1c6aa1de984703bdd5f7ebce8918e1 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T20:43:08Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-cb1c6aa1de984703bdd5f7ebce8918e12023-11-23T22:53:58ZengMDPI AGAxioms2075-16802022-10-01111053710.3390/axioms11100537Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation OperatorsSeng Huat Ong0Choung Min Ng1Hong Keat Yap2Hari Mohan Srivastava3Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, MalaysiaInstitute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, MalaysiaDepartment of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Kajang 43000, MalaysiaDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaThe objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defined. The convergence property of the Bernstein generalization is established. It is also shown that the Cheney–Sharma operator is the Szász–Mirakyan operator averaged by a certain probability distribution.https://www.mdpi.com/2075-1680/11/10/537generalized Laguerre polynomialsKorovkin theoremnoncentral negative binomialprobabilistic derivationWeierstrass approximation theoremSzász–Mirakyan operator |
| spellingShingle | Seng Huat Ong Choung Min Ng Hong Keat Yap Hari Mohan Srivastava Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators Axioms generalized Laguerre polynomials Korovkin theorem noncentral negative binomial probabilistic derivation Weierstrass approximation theorem Szász–Mirakyan operator |
| title | Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators |
| title_full | Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators |
| title_fullStr | Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators |
| title_full_unstemmed | Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators |
| title_short | Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators |
| title_sort | some probabilistic generalizations of the cheney sharma and bernstein approximation operators |
| topic | generalized Laguerre polynomials Korovkin theorem noncentral negative binomial probabilistic derivation Weierstrass approximation theorem Szász–Mirakyan operator |
| url | https://www.mdpi.com/2075-1680/11/10/537 |
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