On the image of the lupaş q-analogue of the bernstein operators

Abstract

The Lupaş q-analogue, Rn,q , is historically the first known q-version of the Bernstein operator. It has been studied extensively in different aspects by a number of authors during the last decades. In this work, the following issues related to the image of the Lupaş q-analogue are discussed: A new explicit formula for the moments has been derived, independence of the image Rn,q from the parameter q has been examined, the diagonalizability of operator Rn,q has been proved, and the fact that Rn,q does not preserve modulus of continuity has been established.