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 inComputational methods and function theory Vol. 25; no. 2; pp. 303 - 315
Main Authors Gürel Yılmaz, Övgü, Ostrovska, Sofiya, Turan, Mehmet
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.06.2025
Subjects
Continuity (mathematics)
Entire functions
Operators (mathematics)
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ISSN1617-9447
2195-3724
DOI10.1007/s40315-024-00534-7

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Summary: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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ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-024-00534-7