The Impact of the Limit q-Durrmeyer Operator on Continuous Functions
The limit q -Durrmeyer operator, $$D_{\infty ,q}$$ D ∞ , q , was introduced and its approximation properties were investigated by Gupta (Appl. Math. Comput. 197(1):172–178, 2008) during a study of q -analogues for the Bernstein–Durrmeyer operator. In the present work, this operator is investigated f...
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| Published in | Computational methods and function theory Vol. 25; no. 2; pp. 303 - 315 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Heidelberg
Springer Nature B.V
01.06.2025
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| Online Access | Get full text |
| ISSN | 1617-9447 2195-3724 |
| DOI | 10.1007/s40315-024-00534-7 |
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| Abstract | The limit q -Durrmeyer operator, $$D_{\infty ,q}$$ D ∞ , q , was introduced and its approximation properties were investigated by Gupta (Appl. Math. Comput. 197(1):172–178, 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 $$D_{\infty ,q}$$ D ∞ , q . The interrelation between the analytic properties of a function f and the rate of growth for $$D_{\infty ,q}f$$ D ∞ , q f are established, and the sharpness of the obtained results are demonstrated. |
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| AbstractList | The limit q-Durrmeyer operator, D∞,q, was introduced and its approximation properties were investigated by Gupta (Appl. Math. Comput. 197(1):172–178, 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∞,q. The interrelation between the analytic properties of a function f and the rate of growth for D∞,qf are established, and the sharpness of the obtained results are demonstrated. The limit q -Durrmeyer operator, $$D_{\infty ,q}$$ D ∞ , q , was introduced and its approximation properties were investigated by Gupta (Appl. Math. Comput. 197(1):172–178, 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 $$D_{\infty ,q}$$ D ∞ , q . The interrelation between the analytic properties of a function f and the rate of growth for $$D_{\infty ,q}f$$ D ∞ , q f are established, and the sharpness of the obtained results are demonstrated. |
| Author | Gürel Yılmaz, Övgü Turan, Mehmet Ostrovska, Sofiya |
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| References | WS Chung (534_CR5) 2021; 60 NI Mahmudov (534_CR13) 2014; 237 534_CR1 FH Jackson (534_CR11) 1910; 41 MM Derriennic (534_CR6) 1981; 31 534_CR7 S Ostrovska (534_CR14) 2016; 69 V Gupta (534_CR9) 2008; 197 GG Lorentz (534_CR12) 1986 V Gupta (534_CR10) 2008; 31 (534_CR4) 1996 J Bustamante (534_CR3) 2017 GM Phillips (534_CR15) 2003 SG Gal (534_CR8) 2009 W Boehm (534_CR2) 1999; 16 J Thomae (534_CR16) 1869; 70 J Zeng (534_CR17) 1994; 25 |
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| Title | The Impact of the Limit q-Durrmeyer Operator on Continuous Functions |
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