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

The Conchy’s formula of entire functions f:Ck→C is used to establish Markov-Bernstein type inequalities of muhivariate polynomials with positive coefficients on the k-dimensional simplex Tk Rk and on the cube [0,1]k.The main results generalize and improve those of G.G.Lorentz,etc.Some applications of these mequal ties are also considered in polynomial constrained approximation.