Smoothness and Shape Preserving Properties of Bernstein Semigroup

摘要

This paper is concerned with the strongly continuous semigroup (T(t)) (t = 0) of operators on C[0, 1] which can be represented as a limit of suitable iterates of the Bernstein operators B-n. We present some new smoothness and shape preserving properties of the operators T(t) and Bn. The asymptotic behavior and simultaneous approximation results are also presented.