若函數f 在實數區間 I 上是凸函數，其中a ,b∈I，則
f((a+b)/2)≤1/(b-a) integral_a^b f(x) dx≤1/2[f(a)+f(b)]是文獻中著名的Hermite-Hadamard不等式。
A.EL FARISSI提出了這樣的問題：若函數f 在實數區間 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≤1/(b-a) integral_a^b f(x) dx≤L≤1/2[f(a)+f(b)]
本文主要研究目的是提供上述問題的一些答案，且導出一些更細化的Hermite-Hadamard不等式。

If f is convex function on [a,b], then
f((a+b)/2)≤1/(b-a) integral_a^b f(x) dx≤1/2[f(a)+f(b)]
is known in the literature called Hermite-Hadamard inequality.
There is the question that if f is convex function on [a,b],
does it exist real l and L such that
f((a+b)/2)≤l≤1/(b-a) integral_a^b f(x) dx≤L≤1/2[f(a)+f(b)]
The major goal of this study is to give some answers to the question,and refinements 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
3.參考文獻………………………………………………………………………………18

[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