若f:[a,b]→ℝ為凸函數且a,b屬於ℝ，則下列不等式
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。
此論文主要是要探討若f在[a,b]中為凸函數，則是否存在實數𝓵和L滿足
 f((a+b)/2) ≤ 𝓵 ≤ 1/(b-a) ∫_a^b f(x)dx ≤ L ≤ 1/2 [f(a)+f(b)]。
   

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.                                                      
This is the classic Hermite-Hadamard inequality.
There is the question that if f is convex on [a,b] whether there exist real numbers 𝓵 and L such that f((a+b)/2) ≤ 𝓵 ≤ 1/(b-a) ∫_a^b f(x)dx ≤ L ≤ 1/2[f(a)+f(b)].                                    

目錄
1.緒論...........1
2.預備定理.......2
3.主要定理.......4
4.參考文獻.......14

[1] S.S DRAGOMIR AND C.E.M PEARCE,Selected Topics on Hermite-Hadamard Inequalites,(RGMIA Monographs http://rgmia.vu.edu.au/monographs/hermite_hadamard.html) ,Victoria University,2000.
[2] A. EL FARISSI, Z.LATREUCH,B.BELAÏDI,Hadamard-Type Inequalities for Twice Differentiable Functions, RGMIA, Research Report Collection,12.1(2009),Art.6.
[3] A.EL FARISSI,Simple proof and refinement of Hermite-Hadamard inequality, Journal of Mathematical Inequalitie,Vol.4,No.3(2010),365-369.
[4] J.HADAMARD, Étude Sur les propriétés des fonctions entières et en particulier d’une function considéréé par Riemann, J.Math.Pures Appl.,58(1893),171-21