MARKOV-BERNSTEIN TYPE INEQUALITIES OF MULTIVARIATE POLYNOMIALS WITH POSITIVE COEFFICIENTS AND APPLICATIONS

摘要

The Cauchy's formula of entire functions f: C~k→C is used to establish Markov-Bernstein type inequalities of multivariate polynomials with positive coefficients on the k-dimensional simplex T_k is contained in R~k and on the cube [0, 1]~k. The main results generalize and improve those of G. G. Lorentz, etc. Some applications: of these inequalities are also considered in polynomial constrained approximation.