RADO 不等式之一些推廣

SOME GENERALIZATIONS OF RADO'S INEQUALITY

何振泰(Chen-Tai Ho)

指導教授 ： 陳功宇

淡江大學/理學院/數學學系碩士班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00747

摘要

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。

關鍵字

Rado不等式 ； 凸函數

並列摘要

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.

並列關鍵字

RADO's inequality ； Convex function ； Popoviciu's inequality ； Bullen inequality

參考文獻

[1]P.S.Bullen, Rado’s inequality, Aequationes Math.,6 (1971),149-156.

[2]Walter Rudin REAL AND COMPLEX ANALYSIS ,1987,62-63.

[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,