函數在區間上是凸函數，就是我們在所熟知關於凸函數的Hermite-Hadamard 不等式 [3,P49]。
在參考文獻[7] Dragomir 及 Agarwal証明了以下的引理。
這份論文的目的是為了要推廣定理B和定理C，並且應用他們在一些特殊的平均數和不規則四邊形的公式上。

Let f be a convex function on the interval  of real numbers and with a<b.The inequalityis well known in the literature as Hermite-Hadamard’s inequality [ 3,P49 ]  
For several recent results concerning Hermite-Hadamard’s inequality, we refer the interested reader to [1-6], where further references are listed.
  In [7] Dragomir and Agarwal proved the following lemma.
  The aim of this paper is to give some generalizations of theorem B and theorem C as well as to apply them to some special means and to trapezoidal formula..

目 次
中文摘要	i
英文摘要	ii
目 次	iii
第壹章  前言	1
第貳章  主要結果	2
第參章  特殊平均數的應用	6
第肆章  梯形公式的應用	13
參考文獻	17
Content
1.Introduction	19
2. Main results	20
3.Application to special means  	24
4.Application to trapezoidal  formula	32
References	37

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2.S. S.Dragomir, J. E. Pacaric, and J. Sandor, A note on the Jensen-Hadamard’s inequality, And. Num. Ther. Approx. 19, 29-34 (1990).
3.S. S. Dragomir, Two mappings in connection to Hadamard’s inequality, J Math. Anal. Appl. 167, 49-56(1992).
4.S. S. Dragomir, On Hadamard’s inequalities, for convex functions, Mat. Balkanica 6, 215-222(1992).
5.S. S. Dragomir and C. Buse, Refinements of Hadamard’s inequality for multiple integrals, Utilitias Math. 47, 193-198(1995).
6.S. S. Dragomir, J. E. Pacaric and L. E Pesaso, Some inequalities of Hadamard type, Soochow J. Math. 21, 335-341(1995).
7.S. S. Dragomir and R. P. Agarwal, Two Inqualities for differentiable Mapings and Aplications to Special Means of Real Number and to Trapezoid Formula, Appl. Math. Leff. Vol II N0.5 91-95 (1998)
8.R. P. Agarwal and S. S. Dragomir, An application of Hayashi’s inequality for differentiable functions, Computers Math. Applic. 32(6),95-99(1996).
9.S. S. Dragomir and S. Wang, Applications of Ostrowaki’s inequality to the estimation of error bounds for some special means and for some numerical quadrature rule, Appl. Math. Lett.11(1), 105-109(1998).
10.S. S. Dragomir and S. Wang, An inequality of Ostrowaki’-Griiss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rule, Computers Math. Applic. 33(11),15-20(1997).
11.S. S. Dragomir and S. Wang, A new inequality of Ostrowaki’s type in   norm and applications to some special means and to some numerical quadrature rule,amkang J. Math. (to appear).