Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties
In this study, we establish a new class of Kantorovich-Stancu type [Formula: see text]Bernstein operators via an adaptation of Bézier bases which are formulated with the inclusion of the shape parameters [Formula: see text], [Formula: see text], and a positive parameter [Formula: see text] First, we...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Mathematical and Computer Modelling of Dynamical Systems |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/13873954.2024.2335382 |
| _version_ | 1826936831563792384 |
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| author | Nezihe Turhan Faruk Özger Mohammad Mursaleen |
| author_facet | Nezihe Turhan Faruk Özger Mohammad Mursaleen |
| author_sort | Nezihe Turhan |
| collection | DOAJ |
| description | In this study, we establish a new class of Kantorovich-Stancu type [Formula: see text]Bernstein operators via an adaptation of Bézier bases which are formulated with the inclusion of the shape parameters [Formula: see text], [Formula: see text], and a positive parameter [Formula: see text] First, we present a uniform convergence result for these operators and, subsequently, examine the convergence properties by utilizing the weighted [Formula: see text]-statistical convergence notion. Furthermore, we estimate the rate of the weighted [Formula: see text]-statistical convergence of these operators. We conclude our work by providing a numerical example with explanatory graphs to show their approximation behaviours. |
| first_indexed | 2024-04-24T09:46:17Z |
| format | Article |
| id | doaj.art-345477bad6aa452eb5326e183f84c843 |
| institution | Directory Open Access Journal |
| issn | 1387-3954 1744-5051 |
| language | English |
| last_indexed | 2025-02-17T18:28:39Z |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Mathematical and Computer Modelling of Dynamical Systems |
| spelling | doaj.art-345477bad6aa452eb5326e183f84c8432024-12-12T14:07:39ZengTaylor & Francis GroupMathematical and Computer Modelling of Dynamical Systems1387-39541744-50512024-12-0130122826510.1080/13873954.2024.2335382Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation propertiesNezihe Turhan0Faruk Özger1Mohammad Mursaleen2Department of Engineering Sciences, Izmir Katip Celebi University, Izmir, TurkeyDepartment of Computer Engineering, Iğdir University, Iğdir, TurkeyDepartment of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, TaiwanIn this study, we establish a new class of Kantorovich-Stancu type [Formula: see text]Bernstein operators via an adaptation of Bézier bases which are formulated with the inclusion of the shape parameters [Formula: see text], [Formula: see text], and a positive parameter [Formula: see text] First, we present a uniform convergence result for these operators and, subsequently, examine the convergence properties by utilizing the weighted [Formula: see text]-statistical convergence notion. Furthermore, we estimate the rate of the weighted [Formula: see text]-statistical convergence of these operators. We conclude our work by providing a numerical example with explanatory graphs to show their approximation behaviours.https://www.tandfonline.com/doi/10.1080/13873954.2024.2335382Statistical rate of convergenceerror analysisshape parameter |
| spellingShingle | Nezihe Turhan Faruk Özger Mohammad Mursaleen Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties Mathematical and Computer Modelling of Dynamical Systems Statistical rate of convergence error analysis shape parameter |
| title | Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties |
| title_full | Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties |
| title_fullStr | Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties |
| title_full_unstemmed | Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties |
| title_short | Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties |
| title_sort | kantorovich stancu type α λ s bernstein operators and their approximation properties |
| topic | Statistical rate of convergence error analysis shape parameter |
| url | https://www.tandfonline.com/doi/10.1080/13873954.2024.2335382 |
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