Starting with a positive linear operator we apply the Kantorovich modification and related modification. The resulting operators are investigated. We interested in eigenstructure, Voronovskaya formula, induced generalized convexity, invariant measures iterates. Some known results from literature extended.

We consider Kantorovich modifications of linking operators and Stancu the classical Bernstein operators. For modified we determine limits iterates invariant measures. In order to find have solve systems linear equations this end use a suitable iterative algorithm.