On the Image of the Lupaş q -Analogue of the Bernstein Operators

The Lupaş q -analogue, R_n,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 R_n,q from the parameter q has been examined, the diagonalizability of operator R_n,q has been proved, and the fact that R_n,q does not preserve modulus of continuity has been established.