Journal of Mathematical Analysis and Applications, vol.529, no.2, 2024 (SCI-Expanded)
Article / Article
Journal of Mathematical Analysis and Applications
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
Lupaş q-analogue, Operator norm, q-integers, Strong operator topology, Uniform operator topology
Recep Tayyip Erdoğan University Affiliated:
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.