H?lder不等式的两种新证法及Cauchy-Schwarz不等式的加细
Two new proof methods of H?lder inequality and a refinement of the Cauchy-Schwarz inequality
施俊 1刘建忠 1彭庆英2
作者信息
- 1. 江苏理工学院数理学院,江苏常州 213001
- 2. 常州技师学院基础部,江苏常州 213018
- 折叠
摘要
Hölder不等式是一类重要的不等式.本文分别利用Cauchy-Schwarz不等式及关于凸函数的Jensen不等式,给出了积分型Hölder不等式的两种新的证明方法.据此,结合受控理论给出Cauchy-Schwarz不等式的一种加细及一个新的反向Hölder不等式.
Abstract
Hölder inequality is an important class of inequalities.By means of Cauchy-Schwarz inequality and Jensen inequality for convex functions,two kinds of new proofs for integral form of Hölder inequality are pre-sented.Based on this,a refinement of Cauchy-Schwarz inequality and a new inverse Hölder inequality are given in combination with the controlled theory.
关键词
Cauchy-Schwarz不等式/Hölder不等式/Jensen不等式/凸函数/Schur凸函数Key words
Cauchy-Schwarz inequality/Hölder inequality/Jensen inequality/convex functions/Schur convex funtions引用本文复制引用
基金项目
2021年江苏省科技厅自然科学基金面上项目(BK20211358)
出版年
2024
NETL
NSTL
万方数据