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系統識別號 U0002-2606201314461900
中文論文名稱 關於兩凸函數乘積的阿達瑪-赫米特不等式的研究
英文論文名稱 On some Hermite-Hadamard inequalities for product of convex functions
校院名稱 淡江大學
系所名稱(中) 中等學校教師在職進修數學教學碩士學位班
系所名稱(英) Executive Master's Program In Mathematics for Teachers
學年度 101
學期 2
出版年 102
研究生中文姓名 謝燦熒
研究生英文姓名 Tsan-Ying Hsieh
學號 700190100
學位類別 碩士
語文別 中文
第二語文別 英文
口試日期 2013-06-21
論文頁數 27頁
口試委員 指導教授-楊國勝
委員-李武炎
委員-曾貴麟
中文關鍵字 凸函數  Hadamard不等式 
英文關鍵字 convex function  Hadamard’s inequalities 
學科別分類
中文摘要 本文的主要目的是推導出一些比(1.2)細緻的不等式
英文摘要 The main purpose of this paper is to give several refinements of the Hadamard’s inequality (1.2) .

論文目次 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
參考文獻 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.
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