# article.page.titleprefix On the injectivity with respect to q of the Lupaş q-transform

## Date

2024-03

## Journal Title

## Journal ISSN

## Volume Title

## Publisher

Quaestiones Mathematicae

## 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.

## 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.

## Keywords

Lupa¸s q-analogue of the Bernstein operators, Lupa¸s q-transform, analytic function, q-periodicity, 47B38, 30A99, 26C15

## Citation

https://hdl.handle.net/20.500.14411/2029