概率论思想在一些不等式中的应用

Application of Probability Theory in Some Inequalities

随着概率论的应用和迅速发展,概率论的应用逐步深入到各个领域,涉足到各个行业。在数学上一些常见的不等式的证明,若运用代数方法较难得到解决,而运用概率方法就可以较方便地得到证明。这种证明方法沟通了不同学科之间的联系。应用概率方法证明不等式,是个很有用的方法,建立适当概率模型,使不等式的证明得到简化。本文主要研究了应用概率论的方法证明代数不等式、积分不等式和相关理论的应用。

With the application and rapid development of probability theory,the probability theory gradually penetrates into various fields,and it gets involved in all sectors.Some common proofs of mathematical inequalities are difficult to be resolved by algebraic methods,but could be more conveniently resolved by probabilistic methods.Such methods of proof communicate the relationship among different disciplines.It＇s a useful way to prove inequality by using probabilistic methods.And the appropriate probability model can be found to simplify the proof of inequality.This paper mainly describes the application of probability theory methods,which prove the algebraic inequalities,integral inequalities and the applications of relative theroies.