Abstract
The Cauchy’s formula of entire functions f:Ck→C is used to establish Markov-Bernstein type inequalities of multivariate polynomials with positive coeffeicients 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 inequalities are also considered in polynomial constrained approximation.
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Xuguang, L. Markov-Bernstein type inequalities of multivariate polynomials with positive coefficients and applications. Approx. Theory & its Appl. 12, 46–66 (1996). https://doi.org/10.1007/BF02849317
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DOI: https://doi.org/10.1007/BF02849317