Bernoulli不等式的控制证明及推广

Majorized Proof and Extensions of Bernoulli's Inequality

利用控制不等式理论并结合分析的方法,给出了经典Bernoulli不等式的3种已知的推广的新的证明。此外,利用初等对称函数的Schur凹性和简单的控制关系建立了该不等式的一种新推广。

By using the theory of majorization and combining with the analysis methods,three known extensions of the classic Bernoulli＇s inequality are proved,and a new extension of this inequality is established by the Schur-concatity of the elementary symmetric functions and simple majoricotions.