Hermite polynomials linking Szász–Durrmeyer operators
The aim of present article is to introduce the Szász-integral type sequences of operators in terms of Hermite polynomials and gamma function. Further, we calculate some estimates at test functions and central moments. Moreover, we discuss uniform convergence theorem and order of approximation via Ko...
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| Published in | Computational & applied mathematics Vol. 43; no. 4 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.06.2024
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 2238-3603 1807-0302 |
| DOI | 10.1007/s40314-024-02752-0 |
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| Abstract | The aim of present article is to introduce the Szász-integral type sequences of operators in terms of Hermite polynomials and gamma function. Further, we calculate some estimates at test functions and central moments. Moreover, we discuss uniform convergence theorem and order of approximation via Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in view of Peetre’s
K
-functional, second order modulus of smoothness and Lipschitz type space. Lastly, bivariate version of these sequences of operators are introduced. Moreover, their rate of convergence and order of approximation are investigated. |
|---|---|
| AbstractList | The aim of present article is to introduce the Szász-integral type sequences of operators in terms of Hermite polynomials and gamma function. Further, we calculate some estimates at test functions and central moments. Moreover, we discuss uniform convergence theorem and order of approximation via Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in view of Peetre’s K-functional, second order modulus of smoothness and Lipschitz type space. Lastly, bivariate version of these sequences of operators are introduced. Moreover, their rate of convergence and order of approximation are investigated. The aim of present article is to introduce the Szász-integral type sequences of operators in terms of Hermite polynomials and gamma function. Further, we calculate some estimates at test functions and central moments. Moreover, we discuss uniform convergence theorem and order of approximation via Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in view of Peetre’s K -functional, second order modulus of smoothness and Lipschitz type space. Lastly, bivariate version of these sequences of operators are introduced. Moreover, their rate of convergence and order of approximation are investigated. |
| ArticleNumber | 223 |
| Author | Yadav, Avinash Kumar Heshamuddin, Md Sinha, Brijesh Kumar Rao, Nadeem Ayman-Mursaleen, Mohammad |
| Author_xml | – sequence: 1 givenname: Mohammad surname: Ayman-Mursaleen fullname: Ayman-Mursaleen, Mohammad organization: School of Information and Physical Sciences, The University of Newcastle – sequence: 2 givenname: Md surname: Heshamuddin fullname: Heshamuddin, Md organization: Department of Natural and Applied Sciences, School of Science and Technology, Glocal University – sequence: 3 givenname: Nadeem orcidid: 0000-0002-5681-9563 surname: Rao fullname: Rao, Nadeem email: nadeem.e14515@cumail.in, nadeemrao1990@gmail.com organization: University Centre for Research and Development, Chandigarh University, Department of Mathematics, University Institute of Sciences, Chandigarh University – sequence: 4 givenname: Brijesh Kumar surname: Sinha fullname: Sinha, Brijesh Kumar organization: School of Information Technology, Artificial intelligence and Cyber security, Rastriya Raksha University – sequence: 5 givenname: Avinash Kumar surname: Yadav fullname: Yadav, Avinash Kumar organization: Department of Applied science, Galgotias College of Engineering and Technology |
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| Cites_doi | 10.1016/1385-7258(88)90007-8 10.1007/s40995-020-01018-8 10.4153/CJM-1953-063-7 10.1007/s40995-020-01024-w 10.6028/jres.045.024 10.1007/s13398-019-00655-y 10.31801/cfsuasmas.941919 10.1155/2023/5245806 10.1007/BF01733787 10.1016/j.kjs.2023.12.007 10.37193/CJM.2016.01.07 10.1007/s002110050413 10.4064/sm218-2-1 10.1016/j.aml.2012.02.043 10.1073/pnas.60.4.1196 10.4153/CJM-1976-123-8 10.3934/math.2024217 10.1016/j.jmaa.2023.127087 10.1016/j.jksus.2024.103120 10.1016/j.cam.2016.12.016 10.1007/s40995-023-01550-3 10.1007/s11075-004-3632-y 10.2298/FIL1301173O 10.1016/j.cam.2004.10.021 10.1007/s41980-023-00815-2 10.1016/S0377-0427(00)00358-7 10.1515/9783110884586 10.1007/978-3-662-02888-9_10 10.1186/s13660-022-02763-7 10.7153/jmi-2022-16-32 |
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| Snippet | The aim of present article is to introduce the Szász-integral type sequences of operators in terms of Hermite polynomials and gamma function. Further, we... |
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| SubjectTerms | Applications of Mathematics Approximation Bivariate analysis Computational Mathematics and Numerical Analysis Convergence Gamma function Hermite polynomials Mathematical analysis Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics Operators (mathematics) Sequences Smoothness Theorems |
| Title | Hermite polynomials linking Szász–Durrmeyer operators |
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