ON THE RATE OF CONVERGENCE FOR THE <i>q</i>-DURRMEYER POLYNOMIALS IN COMPLEX DOMAINS

Gurel Ö., Ostrovska S., Turan M.

MATHEMATICA SLOVACA, cilt.74, sa.5, ss.1267-1276, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 74 Sayı: 5
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1515/ms-2024-0092
  • Dergi Adı: MATHEMATICA SLOVACA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1267-1276
  • Anahtar Kelimeler: q-integers, q-Durrmeyer operator, limit q-Durrmeyer operator, rate of convergence, analytic function
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

The q-Durrmeyer polynomials are one of the popular q-versions of the classical operators of approximation theory. They have been studied from different points of view by a number of researchers. The aim of this work is to estimate the rate of convergence for the sequence of the q-Durrmeyer polynomials in the case 0 < q < 1. It is proved that for any compact set D ⊂ C, the rate of convergence is O(qn) as n → ∞. The sharpness of the obtained result is demonstrated.