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

OpenAlex İngilizce

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 byDuring 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.