這篇論文的主要研究目的是將阿達瑪不等式(1.2)做更進一步的改進。

The main purpose of this paper is to give several refinements of Hermite-Hadamard  inequality(1.2).

目錄
1.導論…………………1
 定理A…………………1
2.主要結果……………1
 定理1…………………1
 備註1…………………5
 定理2…………………5
 備註2…………………13
 定理3…………………13
 備註3…………………31
參考文獻………………32
1. Introduction………34
    Theorem A…………34
2. Main results………34
Theorem 1………………34
 Remark 1………………38
Theorem 2………………38
 Remark 2………………46
Theorem 3………………46
 Remark 3………………64
Reference………………65

Reference
[1]S.S.Dragomir,Two mappings in connection to Hadamard’s inequalities,J.Math.Anal.Appl.,167(1992)49-56.
[2]S.S.Dragomir and R.P.Agarwal,Two inqualities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula,Appl.Math.Lett.,11(1998)91-95.
[3]S.S.Dragomir,Y.J.Cho and S.S.Kim,Inequalities of Hadamard’s type for Lipschitzian mappings and their applicaitions, J.Math.Anal. Appl.,245(2000),489-501
[4]S.S.Dragomir and C.E.M.Pearce, Selected Topics on Hermite -Hadamard  Inequalities and Applications, RGMIA Monographs,Victoria University,2000.Online:[http://www.Staff.vu.edu.au/RGMlA/monographs/hermits_hadamard.html]
[5]S.S.Dragomir and S.Wang,A new inequality of Ostrowski’s type in L  norm and applications to some special means and to some numerical quadrature rule,Tamkang J.Math.,28(1997)239-244.
[6]S.S.Dragomir and S.Wang,Applicaitions of Ostrowski’s inequality to the estimation of error bounds for some special means and for some numerical quadrature rule, Appl.Math.Lett.,11(1998) 1005-109.
[7]H.Hudzik and L.Maligranda, Some remarks on s-convex functions, Aequationes Math.,48(1994),100-111.
[8]U.S. Kirmaci et al.,Hadarmard-type inequalities for s-convex functions,Appl.Math Comp.,193(2007),26-35.
[9]U.S.Kirmaci,Inequalities for differentiable mappings and applicatios to special means of real numbers to midpoint formula, Appl.Math.Comp.,147(2004),137-146.
[10]U.S.Kirmaci and M.E.Ozdemir,On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula,Appl.Math.Comp.,153(2004), 361-368.
[11]M.E.Ozdemir,A theorem on mappings with bounded derivatives with applications to quadrature rules and means,Appl.Math.Comp., 138(2003),425-434.
[12]B.G.Pachpatte.On some inegualities for convex functions RGMIA Res/Coll.6(E)(2003), http://rgmia.vu.edu.au/v6(E).html
[13]C.E.M.Pearce and J.Pečarič,Inequalities for differentiable mappings with application to special means and quadrature formual, Appl.Math.Lett.,13(2000)51-55.
[14]G.S.Yang,D.Y.Hwang and K.L.Tseng,Some inequalities for differentiable convex and concave mappings,Comp.Math.Appl.,47(2004),207-216.