若函數f在區間I上是凸函數，其中a,b∈I，則
f((a+b)/2)≤(∫_a^b▒〖f(x) □(24&dx)〗)/(b-a)≤1/2[f(a)+f(b)]
是在文獻中著名的Hermite-Hadamard不等式。
A.EL FARISSI提出了這樣的問題：若函數f在區間I上是凸函數，a,b∈I，則是否存在兩個實數l和L使得下列不等式成立：
f((a+b)/2)≤l≤(∫_a^b▒〖f(x) □(24&dx)〗)/(b-a)≤L≤1/2[f(a)+f(b)]
本文主要研究目的是提供更多上述問題的答案，並研究積分在不同平均值之間的關係，最後考慮有加權的Hermite-Hadamard不等式，進而整理出類似上述問題中更精緻的Hermite-Hadamard不等式。

If f is convex function on [a,b], then 
f((a+b)/2)≤(∫_a^b▒〖f(x) □(24&dx)〗)/(b-a)≤1/2[f(a)+f(b)] 
is well-known in the literature called Hermite-Hadamard inequality.
The main purpose of this paper is to establish a family of more advancement of Hermite-Hadamard inequality.

1.	第一章 前言…………………………………………………………1
2.	第二章 更精緻的Hermite-Hadamard不等式……………………2
3.	第三章 進一步推廣Hermite-Hadamard不等式…………………11
4.	參考文獻……………………………………………………………20

[1] D.S. Mitrinović and I.B. Lacković, Hermite and convexity, Aequat. Math., 28(1985), 229-232.

[2] S. S. D RAGOMIR AND C. E. M. PEARCE,Selected Topics on Hermite-Hadamard Inequalities,(RGMIA Monographs http://rgmia.vu.edu.au /monographs/hermite hadamard.html),Victoria University, 2000

[3] A.El.Farissi,Simple proof and refinement of Hermite-Hadamard inequality,J.Math ineg.ul4,No.3,(2010)365-369

[4] C. NICULESCU AND L.E. PERSSON,Old and new on the Hermite-Hadamard inequality, Real Analysis Exchange, 2004