On the continuity in <i>q</i> of the family of the limit <i>q</i>-Durrmeyer operators

Yllmaz Ö., Ostrovska S., Turan M.

DEMONSTRATIO MATHEMATICA, cilt.57, sa.1, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 57 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1515/dema-2023-0157
  • Dergi Adı: DEMONSTRATIO MATHEMATICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: operator norm, q-Bernstein operator, q-Durrmeyer operator, strong operator topology, uniform operator topology
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

This study deals with the one-parameter family {D-q}(q is an element of[0,1]) of Bernstein-type operators introduced by Gupta and called the limit q-Durrmeyer operators. The continuity of this family with respect to the parameter q is examined in two most important topologies of the operator theory, namely, the strong and uniform operator topologies. It is proved that {D-q}(q is an element of[0,1]) is continuous in the strong operator topology for all q is an element of [0, 1]. When it comes to the uniform operator topology, the continuity is preserved solely at q = 0 and fails at all q is an element of (0, 1]. In addition, a few estimates for the distance between two limit q-Durrmeyer operators have been derived in the operator norm on C[0, 1].