設 →R為凸函數，則下列不等式成立
        (1.1)
此為眾所周知的Hadamard的雙邊不等式。
本文建立一些不等式(1.1)的推廣。

The following double inequality 
f( )   f(x)dx    (1.1)  
which holds for all convex functions  →R is known in the literature as the Hadamard’s inequality.
We establish some new generalizations of the inequality (1.1).

目錄
中文部份                                               
1.序論                                                 1
2.主要結果                                             1
參考文獻                                              19

English part
1.Introduction                                        21
2. Main Results                                              21
References                                                      36

References
[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 fonction consideree par Riemann , J.Math.Pures appl. 58(1893),171-215.
[5].	H.P.Heiag and L.Maligranda , Chebyshev inequality in function spaces , Real Analgsis Exchange 17(1991/92),211-247.
[6].	L.Maligranda , J.E.Pečarić and L.E.Persson , On some inequalities of the Gruss-Barnes and Borell type , J. Math. Anal. Appl. 187(1994),306-323.
[7].	D.S.Mitrinovie , Analytic Inequalities , Spring. Verlag , Berlin , New Yark 1970.
[8].	J.E.Pecaric and S.S. Dragomir , A generalization of Hadamard’s inequality for Urotonic linear functionals , Radovi Mathematicki 7(1991),103-107.