設 f:I⊆R→R 為凸函數(convex function) ，其中a,b ϵ I ,  a<b，則下列不等式恆成立
f((a+b)/2)≤1/(b-a) ∫_a^b▒f(x)  dx ≤1/2 [f(a)+f(b)]            (1.1)
此為廣為人知的Hadamard雙邊不等式。
    本文試著就此Hadamard雙邊不等式(1.1)，建立一些推廣與更細緻的結果。

the following double inequality
                f((a+b)/2)≤1/(b-a) ∫_a^b▒f(x)  dx≤1/2 [f(a)+f(b)]           (1.1)
holds for all convex function on [a, b] is known in the literature as Hermite-Hadamard (or Hadamard ) inequality.
    The main purpose of this paper is to establish some generalizations and refinements of the inequality (1.1).

目錄
中文部分
1.	緒論	1
2.	預備	2
3.	主要結果	9
參考文獻	23

English Part
1.	Introduction	24
2.	Preliminary	25
3.	Main Results	32
Reference	46

[1].	C. Borell, integral inequalities for generalized concave and convex functions. J. Math. Anal. Appl.43(1973), 419-440.
[2].	C. Borell, Inverse inequalities for concave or generalized concave functions, Report No.44, Department of Mathematics, Uppsala University, 1972.
[3].	S.S. Dragomir, Two Mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl. 167(1992)49-56.
[4].	J.Hadamard, Etude sur Les properties des fonctions entieres et en particulier d’une function consideree par Riemann, J.Math.Pures appl. 58(1893), 171-215.
[5].	D.S.Mistrinovie, Analytic Inequalities, Spring. Verlag, Berlin, New Yark 1970.
[6].	B.G, Pachpatte, Dn Dome Inequalities for convex functions RGMIA Res/Cull. G(E)(2003) http://rgmia.vu.edu.au/v6(E).html.
[7].	C.E.M. Pearce and J.E.Pečarić, Inequalities for differentiable mappings with application to special(means and quadrature formula, Appl. Math Lett. 13(2000) 51-55.
[8].	G.S.Yang, D.Y. Huang and K.L. Tseng, Some inequalities for differentiable convert and concave mappings, Appl. Math comps., 47(2004), 207-216.