設 f : 為凸函數(convex function)，其中a, b I, a< b，則下列不等式恆成立
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，建立一些推廣與更細緻的結果。

The following double inequality
holds for all convex functions on [a, b] is known in the literature as Hermite- Hadamard inequality.
The main purpose of this paper is to establish some generalizations and refinements of the inequality

中文部分
1.緒論...............................................1
2.主要結果...........................................4
3.參考文獻..........................................24

English Part
1.Introduction.......................................25
2.Main Results.......................................29
3.Reference..........................................49

[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, On Some 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 convex and concave mappings, Appl. Math comps., 47(2004), 207-216.

[9].J.L,Wang,Some generalizations and refine ments of Hadamard’s double inequalities,Master Theorem,Dept . 9 Math,Tamkang University, Tamsui, Taiwan, 2013.