  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.
