On the approximation of Kantorovich-type Szàsz-Charlier operators
In this study, we introduce the Kantorovich-type modified Szàsz-Charlier operators and examine their approximation properties within the framework of fractional modeling and control theory. These operators are defined using the Korovkin-type theorem, and their local approximation properties are anal...
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| Language: | English |
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De Gruyter
2025-07-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2025-0144 |
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| author | Karabıyık Ümit Ayık Adem |
| author_facet | Karabıyık Ümit Ayık Adem |
| author_sort | Karabıyık Ümit |
| collection | DOAJ |
| description | In this study, we introduce the Kantorovich-type modified Szàsz-Charlier operators and examine their approximation properties within the framework of fractional modeling and control theory. These operators are defined using the Korovkin-type theorem, and their local approximation properties are analyzed in detail. Additionally, the approximation rate of these operators is estimated using the modulus of continuity and functions in the Lipschitz class. To gain a deeper understanding of their approximation capabilities, we calculate their central moments. Furthermore, the convergence rates are determined based on the modulus of continuity, and a Voronovskaja-type asymptotic formula is provided for these operators. Our study also investigates the approximation speed in weighted spaces, which is crucial for addressing complex dynamical systems in science and engineering. The approximation speed in weighted spaces is evaluated using the weighted modulus of continuity and the Peetre-K function. Finally, illustrative graphics generated using Maple are presented to visualize the convergence of operators to specific functions. |
| format | Article |
| id | doaj-art-1f43c71fc76d4d2bb61a18ba1c78f0d1 |
| institution | Matheson Library |
| issn | 2391-4661 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-1f43c71fc76d4d2bb61a18ba1c78f0d12025-08-04T09:39:14ZengDe GruyterDemonstratio Mathematica2391-46612025-07-0158123924510.1515/dema-2025-0144On the approximation of Kantorovich-type Szàsz-Charlier operatorsKarabıyık Ümit0Ayık Adem1Department of Mathematics and Computer Sciences, Faculty of Sciences, Necmettin Erbakan University, 42090, Konya, TurkeyDepartment of Research Information System, Cumhuriyet University, 58140, Sivas, TurkeyIn this study, we introduce the Kantorovich-type modified Szàsz-Charlier operators and examine their approximation properties within the framework of fractional modeling and control theory. These operators are defined using the Korovkin-type theorem, and their local approximation properties are analyzed in detail. Additionally, the approximation rate of these operators is estimated using the modulus of continuity and functions in the Lipschitz class. To gain a deeper understanding of their approximation capabilities, we calculate their central moments. Furthermore, the convergence rates are determined based on the modulus of continuity, and a Voronovskaja-type asymptotic formula is provided for these operators. Our study also investigates the approximation speed in weighted spaces, which is crucial for addressing complex dynamical systems in science and engineering. The approximation speed in weighted spaces is evaluated using the weighted modulus of continuity and the Peetre-K function. Finally, illustrative graphics generated using Maple are presented to visualize the convergence of operators to specific functions.https://doi.org/10.1515/dema-2025-0144kantorovich-type szàsz-charlier operatorsthe weighted modulus of continuitylocal approximationweighted spacevoronovskaja-type asymptotic formula41a2541a36 |
| spellingShingle | Karabıyık Ümit Ayık Adem On the approximation of Kantorovich-type Szàsz-Charlier operators Demonstratio Mathematica kantorovich-type szàsz-charlier operators the weighted modulus of continuity local approximation weighted space voronovskaja-type asymptotic formula 41a25 41a36 |
| title | On the approximation of Kantorovich-type Szàsz-Charlier operators |
| title_full | On the approximation of Kantorovich-type Szàsz-Charlier operators |
| title_fullStr | On the approximation of Kantorovich-type Szàsz-Charlier operators |
| title_full_unstemmed | On the approximation of Kantorovich-type Szàsz-Charlier operators |
| title_short | On the approximation of Kantorovich-type Szàsz-Charlier operators |
| title_sort | on the approximation of kantorovich type szasz charlier operators |
| topic | kantorovich-type szàsz-charlier operators the weighted modulus of continuity local approximation weighted space voronovskaja-type asymptotic formula 41a25 41a36 |
| url | https://doi.org/10.1515/dema-2025-0144 |
| work_keys_str_mv | AT karabıyıkumit ontheapproximationofkantorovichtypeszaszcharlieroperators AT ayıkadem ontheapproximationofkantorovichtypeszaszcharlieroperators |