In the present paper we study compositions of piecewise linear interpolation operator S?n and Beta-type B?n, namely An:= ?B?n Gn := B?n ? S?n. Voronovskaya type theorems for operators An are proved, substantially improving some corresponding known results. The rate convergence iterates is considered. Some estimates differences between An, Gn, Bn S?n, respectively, given. Also, behaviour on subs...

We consider positive linear operators having the same fundamental functions and different functionals in front of them. For differences involving such operators, we obtain Voronovskaja-type quantitative results. Applications illustrating theoretical aspects are presented.