若f:[a,b]→R為凸函數，a,b∈R，則
f(a+b/2)≤1/(b-a) ∫_a^bf(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^bf(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^bf(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^bf(x)dx≤L≤f(a)+f(b)/2
The major goal of this study is to give some answers to the question.

目錄：
1. 引言………………………………………………………………………………………1
2. 主要結果…………………………………………………………………………………5
3. 文獻探討…………………………………………………………………………………17

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