The Impact of the Limit q-Durrmeyer Operator on Continuous Functions

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GÜREL YILMAZ Ö., Ostrovska S., Turan M.

Computational Methods and Function Theory, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s40315-024-00534-7
  • Dergi Adı: Computational Methods and Function Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: 30B40, 30D15, 47B38, Analytic function, Entire function, Growth estimates, q-Durrmeyer operator
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

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.