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

Yılmaz Ö., Ostrovska S., Turan M.

Quaestiones Mathematicae, cilt.47, sa.3, ss.477-487, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.2989/16073606.2023.2229556
  • Dergi Adı: Quaestiones Mathematicae
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.477-487
  • Anahtar Kelimeler: analytic function, Lupaş q-analogue of the Bernstein operators, Lupaş q-transform, q-periodicity
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

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.