在本文中，主要以系統化的方式整合文獻資料中與Rado不等式及Popoviciu不等式有相關的不等式。以更簡易的方法(如Jensen不等式和凸函數基本性質)去證明，最後再舉一些例子說明。

In this article, mainly in the systematic way to with the Rado's inequality and Popoviciu's inequalities are related to inequality. More simple methods (such as Jensen's inequality and the fundamental property of convex functions) to prove. 
Finally, give some examples.

1. 前言.............................1

2. 主要結果.........................2

3. 討論............................13

4. 參考文獻.........................17

[1]P.S.Bullen, Rado’s inequality, Aequationes Math.,6 (1971),149-156.
	
[2]Walter Rudin REAL AND COMPLEX ANALYSIS ,1987,62-63.

[3]Vasile Mihesan, Inequality for weighted power pseudo means, Journal of Inequality in Pure and Applied Mathematics,Vol6, Issue 3, Article 75(2005).

[4]Shanhe Wu and Lokenath Debnath, Weighted generalization of Rado’s Inequality and Popoviciu’s inequality, AppliedMathematics Letters21(2008),pp.313-319.

[5]Shanhe Wu, On a weighted and exponential generalization of Rado’s Inequality,Taiwan journal of mathematics, Vol.13, 
No.1,pp.359-368,2009.
 
[6]文開庭與楊清春,Rado不等式與Popovic不等式統一形式的加權推廣及其演 化,毕节師范高等專科學校學報(Journal of buie teachers college),
第十八卷第3期,2000年9月.