某些经典不等式的积分形式及其应用 摘要 在初等数学中有许多重要的不等式,它们在数学分析中有许多积分形式的推广,本文主要介绍均值不等式、不等式、不等式、不等式、不等式和不等式,这些不等式之间也有一定的联系,利用不等式可以推导出均值不等 式 的 推 广 形 式 , 利 用 均 值 不 等 式 可 以 证 明不 等 式 ,不 等 式 可 以 看 成 是不等式的推广,而在不等式的基础上我们又可以证明 不等式.本文主要总结和研究了这些经典不等式的积分形式和推广,从易到难.这些不等式在数学分析中有着广泛的运用,当我们研究积分不等式的时候，可以与生活知识结合起来.关键词 均值不等式 不等式 不等式 不等式 不等式 不等式Abstract There are many important inequalities in elementary mathematics，and they have many generalizations of integral forms in mathematical analysis. This paper mainly introduces mean inequality，Cauchy Schwarz inequality，Jensen inequality，Young inequality，Hölder inequality and Minkowski inequality，which are also related to each other. The generalization of mean inequality can be deduced by Jensen inequality In the form of mean inequality，we can prove Young inequality，Hölder inequality can be regarded as the generalization of Cauchy inequality， and on the basis of Hölder inequality，we can prove Minkowski inequality. This paper mainly summarizes and studies the integral forms and generalizations of these classical inequalities， from easy to difficult. These inequalities are widely used in mathematical analysis. When we study integral inequality, we can combine it with life knowledge.Key words Mean inequality Cauchy Schwarz inequality Jensen inequality Young inequality Hölder inequality Minkowski inequality目 录摘要....................................................................................2Abstract................................................................................21. 均值不等式...............................
