article.page.titleprefix On the injectivity with respect to q of the Lupaş q-transform
| dc.contributor.author | Gürel Yılmaz, Övgü | |
| dc.contributor.author | Ostrovska, Sofiya | |
| dc.contributor.author | Turan, Mehmet | |
| dc.date.accessioned | 2024-05-09T12:31:35Z | |
| dc.date.available | 2024-05-09T12:31:35Z | |
| dc.date.issued | 2024-03 | |
| dc.description | Published by Quaestiones Mathematicae; https://doi.org/10.2989/16073606.2023.2229556; Övgü Gürel Yılmaz, Recep Tayyip Erdogan University, Department of Mathematics, 53100, Rize, Turkey; Sofiya Ostrovska, Mehmet Turan, Atilim University, Department of Mathematics, Incek 06836, Ankara, Turkey. | |
| dc.description.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 \begin{align*} \Lambda_q(f;x)=\prod_{k=0}^{\infty}\frac{1}{1+q^{k}x}\sum_{k=0}^{\infty} \frac{f(1-q^k)q^{k(k-1)/2}x^k}{(1-q)(1-q^2)\ldots(1-q^k)}, \quad x \geqslant 0. \end{align*} 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 Λq with respect to parameter q. More precisely, the conditions on f such that equality Λq (f ; x) = Λr (f ; x), x ⩾ 0 implies q = r have been established. | |
| dc.identifier.citation | https://hdl.handle.net/20.500.14411/2029 | |
| dc.identifier.issn | 1727-933X | |
| dc.identifier.uri | https://doi.org/10.2989/16073606.2023.2229556 | |
| dc.language.iso | en | |
| dc.publisher | Quaestiones Mathematicae | |
| dc.relation.ispartofseries | 47; 3 | |
| dc.subject | Lupa¸s q-analogue of the Bernstein operators | |
| dc.subject | Lupa¸s q-transform | |
| dc.subject | analytic function | |
| dc.subject | q-periodicity | |
| dc.subject | 47B38 | |
| dc.subject | 30A99 | |
| dc.subject | 26C15 | |
| dc.title | On the injectivity with respect to q of the Lupaş q-transform | |
| dc.type | Article | |
| dspace.entity.type | Article |