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, vol.529, no.2, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 529 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.1016/j.jmaa.2022.126842
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Keywords: Lupaş q-analogue, Operator norm, q-integers, Strong operator topology, Uniform operator topology
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

The Lupaş q-analogue Rn,q of the Bernstein operator is the first known q-version of the Bernstein polynomials. It had been proposed by A. Lupaş 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→∞ have been considered.