Equivalency condition of symmetric inequalities

Jingjun Han High school affiliated to Fudan University

S.-T. Yau High School Science Awarded Papers mathscidoc:1608.35008

This paper researches on the judgment theorem and proof of the equivalency condition of a class of symmetric inequalities. By controlling two elementary symmetric polynomials and using the monotonicity of functions and Jensen inequality, it finds the necessary and sufficient condition of the equivalency a class of three-variable and n-variables symmetric inequalities. And we illustrate the application of this method in proof of these inequalities. Then we obtain several judgment theorems on symmetric and cyclic inequalities.
inequality;symmetric;cyclic;three-variables;n-variables;Judgment theorem of the equivalency condition
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  title={Equivalency condition of symmetric inequalities},
  author={Jingjun Han},
Jingjun Han. Equivalency condition of symmetric inequalities. 2008. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160813215154468955055.
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