| Author Name | Affiliation | Postcode | | Anjali* | Department of Applied Science and Humanities,School of Enginnering & Technology, Vivekanananda Institute of Professional Studies-Technical Campus, Delhi 110034, India | 110034 | | Man Singh Beniwal | Department of Applied Science, Maharaja Surajmal Institute of Technology New Delhi 110058, India | 110058 | | Mohd Atif Wahid | Department of Applied Science and Humanities,School of Enginnering & Technology, Vivekanananda Institute of Professional Studies-Technical Campus, Delhi 110034, India | 110034 |
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| Abstract: |
| This study uses the classical orthogonal Laguerre polynomial as a foundation for constructing new operators. We present the Laguerre-Paltanea operator based on the modified Laguerre polynomial that facilitates the approximation of integrable functions. Furthermore, some new discrete and integral-type operators derived from the combination of the Laguerre operator, Laguerre-P?lt?nea operator, and Szász-Mirakyan operator are proposed. We compare the error values of operators and emphasize which operator provides the best approximation. Ultimately, Mathematica software is utilized to generate graphs and infer the convergence of the stated operators to a function for various parameter values under consideration. Additionally, we compare each specified operator and observe that the proposed Laguerre-Pǎltǎnea operator offers a better approximation than the other potential compositions. |
| Key words: Laguerre polynomial convergence properties Păltănea operators error |
| DOI：10.11916/j.issn.1005-9113.2025095 |
| Clc Number:O174 |
| Fund: |
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| Descriptions in Chinese: |
| This study uses the classical orthogonal Laguerre polynomial as a foundation for constructing new operators. We present the Laguerre-Paltanea operator based on the modified Laguerre polynomial that facilitates the approximation of integrable functions. Furthermore, some new discrete and integral-type operators derived from the combination of the Laguerre operator, Laguerre-P?lt?nea operator, and Szász-Mirakyan operator are proposed. We compare the error values of operators and emphasize which operator provides the best approximation. Ultimately, Mathematica software is utilized to generate graphs and infer the convergence of the stated operators to a function for various parameter values under consideration. Additionally, we compare each specified operator and observe that the proposed Laguerre-Pǎltǎnea operator offers a better approximation than the other potential compositions. |
