The Proof of Four Families of Twin Symmetric Inequalities
The results of a pair of twin symmetric inequalities are generalized,and four families of twin symmetric inequalities are obtained and proved as well.By applying the arithmetic-geometric mean inequality,the proof of the first two families of symmetric inequalities is successfully completed.However,it is no longer possible to use the arithmetic-geometric mean inequality alone when proving the latter two families of symmetric inequalities.With the help of the properties of Popoviciu's inequality and convex function,the difficulty of proof is overcome,and the conclusion of symmetric inequality between the latter two families is proved.
algorithm-geometric mean inequalityPopoviciu inequalitysymmetric inequalityconvex function
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