Markov-Bernstein type inequalities of multivariate polynomials with positive coefficients and applications

The Cauchy’s formula of entire functions f:C^k→C is used to establish Markov-Bernstein type inequalities of multivariate polynomials with positive coeffeicients on the k-dimensional simplex T_k⊂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.