Abstract

Cauchy inequality is a very important inequality in mathematics and physics, especially has wild application in resolving
the proof of inequalities, which has significance for researching inequalities in mathematics. This paper promotes the
original Cauchy inequality. The original n-dimension and 2-order Cauchy inequality is promoted to a n-dimension and
m-order Cauchy inequality and the rigorous proof is also given. Simultaneously, this paper summarizes several corollaries
for this n-dimension and m-order Cauchy inequality, and gives the corresponding proof.

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