1.設f:[a,b]→R是一個定義在[a,b]的凸函數，則

f((a+b)/2) ≤  1/(b-a) ∫f(x)dx  ≤  (f(a)+f(b))/2 

就是著名的Hermite-Hadamard不等式。

2.若f:[a,b]→R 是一個定義在[a,b]的凸函數，則
是否存在兩個實數l和L 
使得  f((a+b)/2)  ≤ l ≤  1/(b-a) ∫f(x)dx ≤  L ≤  (f(a)+f(b))/2   成立
    
3.這個論文主要目的是為了提供更多l和L的答案。

1.If  f : [a,b] → R,  f  is a convex function on [a,b] ,then
f((a+b)/2)≤1/(b-a) ∫f(x)dx≤(f(a)+f(b))/2
This is the classic Hermite-Hadamard inequality.

2.If  f  is a convex function on closed interval [a,b] , do there exist real numbers l and L such that 
f((a+b)/2)  ≤ l ≤  1/(b-a) ∫f(x)dx ≤  L ≤  (f(a)+f(b))/2  ?

3.The purpose of this paper is to find more l and L to satisfy the above inequality .

(一)	Introduction ………………………………………………. 1
(二)	Main result ……………………………………………….. 2
(三)	Reference  ……………………………………………….. 23

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[6] A.EL FARISSI,Simple proof and refinement of Hermite-Hadamard inequality,Journal of Mathematical Inequalities Vol.4 No.3 (2010),365-369.