Jingjun HanHigh school affiliated to Fudan University
Dongrun-Yau Awarded Papersmathscidoc: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