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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.01109 |
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| _version_ | 1866911745588592640 |
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| author | Yılmaz, Övgü Gürel Ostrovska, Sofiya Turan, Mehmet |
| author_facet | Yılmaz, Övgü Gürel Ostrovska, Sofiya Turan, Mehmet |
| contents | The limit $q$-Durrmeyer operator, $D_{\infty,q},$ was introduced and its approximation properties were investigated by V. Gupta in 2008 during a study of $q$-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of $D_{\infty,q}$. The interrelation between the analytic properties of a function $f$ and the rate of growth for $D_{\infty,q}f$ are established, and the sharpness of the obtained results are demonstrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01109 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The impact of the limit $q$-Durrmeyer operator on continuous functions Yılmaz, Övgü Gürel Ostrovska, Sofiya Turan, Mehmet Complex Variables The limit $q$-Durrmeyer operator, $D_{\infty,q},$ was introduced and its approximation properties were investigated by V. Gupta in 2008 during a study of $q$-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of $D_{\infty,q}$. The interrelation between the analytic properties of a function $f$ and the rate of growth for $D_{\infty,q}f$ are established, and the sharpness of the obtained results are demonstrated. |
| title | The impact of the limit $q$-Durrmeyer operator on continuous functions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2401.01109 |