The continuity in q of the Lupaş q-analogues of the Bernstein operators

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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.529, sa.2, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 529 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.jmaa.2022.126842
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Lupaş q-analogue, Operator norm, q-integers, Strong operator topology, Uniform operator topology
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

The Lupas q-analogue Rn,q of the Bernstein operator is the first known q-version of the Bernstein polynomials. It had been proposed by A. Lupas in 1987, but gained the popularity only 20 years later, when q-analogues of classical operators pertinent to the approximation theory became an area of intensive research. In this work, the continuity of operators Rn,q with respect to parameter q in the strong operator topology and in the uniform operator topology has been investigated. The cases when n is fixed and n -> infinity have been considered. (c) 2022 Elsevier Inc. All rights reserved.