Criterions on Equality of Symmetric Inequalities(II)

Jingjun Han High School Affiliated to Fudan University

S.-T. Yau High School Science Awarded Papers mathscidoc:1608.35018

In this paper, we continues to investigate the properties of symmetric inequalities. We study the necessary condition for the extremum to be attained in a semi-algebraic system. From which, we partly solve the problem of the further generalization of Jensen inequality which the author brought up in the previous article. Namely, by using the sign of the (n+1)^th derivative while xing the value of the sum of power of n variables, we get a dimension-descending method. Further, we prove that the necessary and sucient condition for the symmetric inequality of degree m with n variables to hold on R+n is that it holds when the number of nonzero variables does not exceed max&{1, frac{m}{2}}&.
symmetric inequality, dimension-descending method, Jensen inequality
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  title={Criterions on Equality of Symmetric Inequalities(II)},
  author={Jingjun Han},
Jingjun Han. Criterions on Equality of Symmetric Inequalities(II). 2010.
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