若f:[a,b]→R為凸函數，a,b∈R，則
f((a+b)/2)≤1/(b-a)  ∫_a^b f(x)dx≤(f(a)+f(b))/2
恆成立，這就是著名的Hermite-Hadamard雙邊不等式，要探
討的是，若f在[a,b]中的凸函數，則是否存在兩實數l及L 
使得下列不等式能成立：
f((a+b)/2)≤l≤1/(b-a)  ∫_a^b f(x)dx≤L≤(f(a)+f(b))/2      
本論文研究的主要目的是要對上式提供一些解。

If f:[a,b]→R is convex on [a,b], then
f((a+b)/2)≤1/(b-a)  ∫_a^b f(x)dx≤(f(a)+f(b))/2
is known in the literature the Hermite-Hadamard inequality.
There is the question that if f is a convex function on [a,b]
do there exist real numbers l and L such that
f((a+b)/2)≤l≤1/(b-a)  ∫_a^b f(x)dx≤L≤(f(a)+f(b))/2
The major goal of this study is to give some answers to the question.

1. 引言……………………………………………………………………………………1
2. 引理……………………………………………………………………………………3
3. 主要定理………………………………………………………………………………6
	定理3.1………………………………………………………………………………6
	定理3.2………………………………………………………………………………14
	定理3.3………………………………………………………………………………18
4. 結果與討論……………………………………………………………………………21
5. 文獻探討………………………………………………………………………………22

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