若f：[a, b]→R 為凸函數，a,b∈R，
f((a+b)/2) ≤ 1/(b-a) ∫ f(x) dx ≤ 1/2 [f(a)+f(b)] 
成立，這就是Hermite Hadamard不等式，
要探討
若f為[a, b]中的凸函數
是否能找到實數l及L使不等式成立

f((a+b)/2) ≤ l ≤ 1/(b-a) ∫ f(x) dx ≤ L≤ 1/2 [f(a)+f(b)] 

此論文研究主要的目的是要提供更精細的解釋。

If
f：[a, b]→R is convex on [a, b],
f((a+b)/2) ≤ 1/(b-a) ∫ f(x) dx ≤ 1/2 [f(a)+f(b)] 
is the Hermite-Hadamard inequality. 
I  am going to find out whether there are exist numbers l and L if  f  is a convex number on [a,b]

f((a+b)/2) ≤ l ≤ 1/(b-a) ∫ f(x) dx ≤ L≤ 1/2 [f(a)+f(b)] 


The major goal of this study is to give improvement answers to the question.

1.      緒  論 …………………………………………1
2.	預備定理………………………………………2
3.	主要結果………………………………………3
4.	參考文獻………………………………………25

[1]		S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities, (RGMIA Monographs http: / /rgmia.vu.edu.au /monographs/ hermite_hadamard html),Victoria University, 2000.

[2]		A El Farissi, Simple proof and refinement of Hermite-Hadamard inequality, J.Math Ineq.Vol.4, No.3 (2010) 365

[3]	D.S. Mitrinović and I.B. Lacković, Hermite and convexity,
Aequationes Math., 28(1985), 229-232

[4]	C. Niculescu and L.-E. Persson, Old and new on the
Hermite-Hadamard inequality, Real Analysis Exchange, 2004

[5]	方矅 ( 2017 ) .”有關更精細的 Hermite-Hadamard 不等式”，淡江大學數學學系數學所碩士論文