On the Iterates of Some Bernstein-Type Operators*

In this paper, we establish two basic functional-type identities between the iterates of the Bleimann]Butzer]Hahn operator and those of the Bernstein operator, on the one hand, and the iterates of the modified.Meyer]K¨onig and Zeller operator and those of the Baskakov operator, on the other. These identities allow us to transfer the properties of these operators from one to another. Attention is focused on the limit behavior of the iterates and the linear combinations of iterates of Fej´er]Korovkin type