Lagrange-type operators associated with $U_n^{\varrho}$

Heiner Gonska, Ioan Raşa, Elena-Dorina Stănilă

Published 2014-02-20Version 1

We consider a class of positive linear operators which, among others, constitute a link between the classical Bernstein operators and the genuine Bernstein-Durrmeyer mappings. The focus is on their relation to certain Lagrange-type interpolators associated to them, a well known feature in the theory of Bernstein operators. Considerations concerning iterated Boolean sums and the derivatives of the operator images are included. Our main tool is the eigenstructure of the members of the class.