General binomial-type coefficients in the sequence of Bernstein operators

In this paper we study the sequence of Bernstein operators in the case when the binomial coefficients are substituted by general ones satisfying a similar recursive rule. Besides the characterization of the convergence and the approximation properties of the sequence of operators obtained in this manner, the main application regards the approximation of the solutions of suitable second-order parabolic problems. Work performed under the auspices of G. N. A. F. A. (C. N. R.) and M. U. R. S. T.