本文的主要目的是推導出一些比(1.2)細緻的不等式

The main purpose of this paper is to give several refinements of the Hadamard’s　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  …………………………………………………………4
定理 2  …………………………………………………………4  
備註 2  …………………………………………………………6
定理 3  …………………………………………………………6
備註 3  …………………………………………………………9
定理 4  …………………………………………………………9
備註 4  …………………………………………………………10
推論 5  …………………………………………………………10
推論 6  …………………………………………………………10
推論 7  …………………………………………………………11
參考文獻  ………………………………………………………12
1.Introduction…………………………………………………14
Theorem A ………………………………………………………14  
2 Main Results…………………………………………………15 
Theorem 1 ………………………………………………………15
Remark 1  ………………………………………………………17
Theorem 2 ………………………………………………………17
Remark 2  ………………………………………………………20
Theorem 3 ………………………………………………………20
Remark 3  ………………………………………………………22
Theorem 4 ………………………………………………………23
Remark 4  ………………………………………………………23
Corollary 5 ……………………………………………………24
Corollary 6 ……………………………………………………24
Corollary 7 ……………………………………………………24
References  ……………………………………………………26

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 applications, 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 inequalities for convex functions RGMIA Res/Coll.6(E)(2003), http://rgmia,vu.edu.au/v6(E).html

[13]C.E.M.Pearce and J. Pečarić,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.