Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals
The main purpose of this paper is to introduce a new family of parametric Kantorovichtype operators on the half-bounded interval. The convergence properties of these new operators are investigated. The Voronovskaja-type weak inverse theorem and the rate of uniform convergence are obtained. Furthermo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/24/4997 |
| _version_ | 1797380119233298432 |
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| author | Hui Dong Qiulan Qi |
| author_facet | Hui Dong Qiulan Qi |
| author_sort | Hui Dong |
| collection | DOAJ |
| description | The main purpose of this paper is to introduce a new family of parametric Kantorovichtype operators on the half-bounded interval. The convergence properties of these new operators are investigated. The Voronovskaja-type weak inverse theorem and the rate of uniform convergence are obtained. Furthermore, we obtain some shape preserving properties of these operators, including monotonicity, convexity, starshapeness, and semi-additivity preserving properties. Finally, some numerical illustrative examples show that these new operators have a better approximation performance than the classical ones. |
| first_indexed | 2024-03-08T20:33:43Z |
| format | Article |
| id | doaj.art-4152290f8f614f14ae39e755c14748fb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T20:33:43Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4152290f8f614f14ae39e755c14748fb2023-12-22T14:23:33ZengMDPI AGMathematics2227-73902023-12-011124499710.3390/math11244997Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded IntervalsHui Dong0Qiulan Qi1School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, ChinaSchool of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, ChinaThe main purpose of this paper is to introduce a new family of parametric Kantorovichtype operators on the half-bounded interval. The convergence properties of these new operators are investigated. The Voronovskaja-type weak inverse theorem and the rate of uniform convergence are obtained. Furthermore, we obtain some shape preserving properties of these operators, including monotonicity, convexity, starshapeness, and semi-additivity preserving properties. Finally, some numerical illustrative examples show that these new operators have a better approximation performance than the classical ones.https://www.mdpi.com/2227-7390/11/24/4997Kantorovich-type operatorspositive theoremthe Voronovskaja type weak inverse theoremshape preserving property |
| spellingShingle | Hui Dong Qiulan Qi Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals Mathematics Kantorovich-type operators positive theorem the Voronovskaja type weak inverse theorem shape preserving property |
| title | Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals |
| title_full | Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals |
| title_fullStr | Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals |
| title_full_unstemmed | Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals |
| title_short | Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals |
| title_sort | approximation properties of parametric kantorovich type operators on half bounded intervals |
| topic | Kantorovich-type operators positive theorem the Voronovskaja type weak inverse theorem shape preserving property |
| url | https://www.mdpi.com/2227-7390/11/24/4997 |
| work_keys_str_mv | AT huidong approximationpropertiesofparametrickantorovichtypeoperatorsonhalfboundedintervals AT qiulanqi approximationpropertiesofparametrickantorovichtypeoperatorsonhalfboundedintervals |