The Impact of the Limit <i>q</i>-Durrmeyer Operator on Continuous Functions

Gürel Yılmaz Ö., Ostrovska S., Turan M.

COMPUTATIONAL METHODS AND FUNCTION THEORY, cilt.25, sa.2, ss.303-315, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 2
  • Basım Tarihi: 2025
  • 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
  • Sayfa Sayıları: ss.303-315
  • Anahtar Kelimeler: Analytic function, Entire function, Growth estimates, q-Durrmeyer operator
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

The limit q-Durrmeyer operator, D-infinity,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-infinity,D-q. The interrelation between the analytic properties of a function f and the rate of growth for D(infinity,q)f are established, and the sharpness of the obtained results are demonstrated.