若f:[a,b]→R為凸函數，則：
f((a+b)/2)≤1/(b-a) ∫a^b〖f(x)dx〗≤1/2[f(a)+f(b)]
恆成立，此不等式稱為Hermite-Hadamard不等式。
而更進一步去討論是否存在兩實數l及L使得
f((a+b)/2)≤l≤1/(b-a) ∫a^b〖f(x)dx〗≤L≤1/2[f(a)+f(b)]的問題中，本論文研究的目的在提出此問題的一些解。

If f:[a,b]→R is convex on [a,b], then the inequality
f((a+b)/2)≤1/(b-a) ∫a^b〖f(x)dx〗≤1/2[f(a)+f(b)] holds. The inequality is called the Hermite-Hadamard inequality. To further discuss whether there are two real numbers 
l and L that satisfy this inequality
f((a+b)/2)≤l≤1/(b-a) ∫a^b〖f(x)dx〗≤L≤1/2[f(a)+f(b)] , the purpose of this paper is to propose some solutions to this problem.

謝誌 ........................................ i
摘要 ....................................... ii
Abstract .................................. iii
目錄 ....................................... iv
第一章 引言 ................................. 1
第二章 主要結果 ............................. 2
第三章 參考文獻 ............................ 10

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