ON THE INJECTIVITY WITH RESPECT TO <i>q</i> OF THE LUPAS <i>q</i>-TRANSFORM

Yılmaz Ö., Ostrovska S., Turan M.

QUAESTIONES MATHEMATICAE, cilt.47, sa.3, ss.477-487, 2024 (SCI-Expanded, Scopus) identifier 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 Lupas q-transform has first appeared in the study of the Lupas q-analogue of the Bernstein operator. Given 0 < q < 1 and f is an element of C[0, 1], the Lupas q-transform is defined by Lambda(q)(f; x) Pi(infinity)(k=0) 1/1 + q(k)x Sigma(k=0)f(1 - q(k))q(k(k-1)/2)x(k)/(1 - q)(1 - q(2)) center dot center dot center dot (1 - q(k)), x >= 0. 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 Lambda(q) with respect to parameter q. More precisely, the conditions on f such that equality Lambda(q)(f; x) = Lambda(r)(f; x); x >= 0 implies q = r have been established.