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中文論文名稱 兩凸函數乘積的阿達瑪-赫米特不等式的一些結果
英文論文名稱 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 陳韋建
研究生英文姓名 Wei-Chien Chen
學號 700190068
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 66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  Hermite-Hadamard不等式 
英文關鍵字 convex function  Hermite-Hadamard inequalities 
學科別分類
中文摘要 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。
英文摘要 The main purpose of this paper is to give several refinements of Hermite-Hadamard 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…………………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

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 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.
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