Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type Polynomials
This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence and the rate of approximation are analyzed using the classical...
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MDPI AG
2025-03-01
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| author | Nadeem Rao Mohammad Farid Mohd Raiz |
| author_facet | Nadeem Rao Mohammad Farid Mohd Raiz |
| author_sort | Nadeem Rao |
| collection | DOAJ |
| description | This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence and the rate of approximation are analyzed using the classical Korovkin theorem and the modulus of continuity for Lebesgue measurable and continuous functions. A Voronovskaja-type theorem is also established to approximate functions with first- and second-order continuous derivatives. Numerical and graphical analyses are presented to support these findings. Furthermore, a bivariate sequence of these operators is introduced to approximate a bivariate class of Lebesgue measurable and continuous functions in two variables. Finally, numerical and graphical representations of the error are provided to check the rapidity of convergence. |
| format | Article |
| id | doaj-art-d88cbc6b42b2492ab360d122848e7f0a |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-d88cbc6b42b2492ab360d122848e7f0a2025-08-20T02:24:39ZengMDPI AGAxioms2075-16802025-03-0114425210.3390/axioms14040252Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type PolynomialsNadeem Rao0Mohammad Farid1Mohd Raiz2Department of Mathematics, University Center for Research and Development, Chandigarh University, Mohali 140413, Punjab, IndiaDepartment of Mathematics, College of Science, Qassim University, Saudi ArabiaDepartment of Applied Science and Humanities, Global Institute of Technology and Management, 5 KM Mile Stone, Haily Mandi Road, Kheda Khurampur, Farrukhnagar, Gurugramn 122506, Haryana, IndiaThis research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence and the rate of approximation are analyzed using the classical Korovkin theorem and the modulus of continuity for Lebesgue measurable and continuous functions. A Voronovskaja-type theorem is also established to approximate functions with first- and second-order continuous derivatives. Numerical and graphical analyses are presented to support these findings. Furthermore, a bivariate sequence of these operators is introduced to approximate a bivariate class of Lebesgue measurable and continuous functions in two variables. Finally, numerical and graphical representations of the error are provided to check the rapidity of convergence.https://www.mdpi.com/2075-1680/14/4/252Frobenius polynomialsmathematical operatorsrate of convergenceVoronovskaja theoremmodulus of smoothnessapproximation algorithms |
| spellingShingle | Nadeem Rao Mohammad Farid Mohd Raiz Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type Polynomials Axioms Frobenius polynomials mathematical operators rate of convergence Voronovskaja theorem modulus of smoothness approximation algorithms |
| title | Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type Polynomials |
| title_full | Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type Polynomials |
| title_fullStr | Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type Polynomials |
| title_full_unstemmed | Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type Polynomials |
| title_short | Approximation Results: Szász–Kantorovich Operators Enhanced by Frobenius–Euler–Type Polynomials |
| title_sort | approximation results szasz kantorovich operators enhanced by frobenius euler type polynomials |
| topic | Frobenius polynomials mathematical operators rate of convergence Voronovskaja theorem modulus of smoothness approximation algorithms |
| url | https://www.mdpi.com/2075-1680/14/4/252 |
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