ON THE DECOMPOSITION OF BERNSTEIN OPERATORS

Let F-n be the linear operators on C[0, 1] defined by B-n = B-n circle F(n)where B-n are the classical Bernstein operators and (B) over bar (n) are Beta operators. This decomposition of B-n was investigated in Gonska et al. [6]. Although the operators F-n are not positive, they have quite interesting properties. We obtain new results concerning the convergence of the sequence (F-n). An associated quadrature formula with positive coefficients and equidistant knots is investigated, as well as the eigenstructure of F-n.