On the injectivity with respect to q of the Lupaş q-transform


Yılmaz Ö., Ostrovska S., Turan M.

Quaestiones Mathematicae, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.2989/16073606.2023.2229556
  • Journal Name: Quaestiones Mathematicae
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Keywords: analytic function, Lupaş q-analogue of the Bernstein operators, Lupaş q-transform, q-periodicity
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

The Lupaş q-transform has first appeared in the study of the Lupaş q-analogue of the Bernstein operator. Given 0 < q < 1 and f ∈ C [0, 1], the Lupaş q-transform is defined by (Figure presented.) During the last decades, this transform has been investigated from a variety of angles, including its analytical, geometric features, and properties of its block functions along with their sums. As opposed to the available studies dealing with a fixed value of q, the present work is focused on the injectivity of Λ q with respect to parameter q. More precisely, the conditions on f such that equality Λ q (f; x) = Λ r (f; x), x ⩾ 0 implies q = r have been established.