系統識別號 | U0002-2906201300302000 |
---|---|
DOI | 10.6846/TKU.2013.01208 |
論文名稱(中文) | 一些Hadamard不等式更細緻的結果 |
論文名稱(英文) | Some refinements of Hadamard’s inequalities |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 中等學校教師在職進修數學教學碩士學位班 |
系所名稱(英文) | Executive Master's Program In Mathematics for Teachers |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 101 |
學期 | 2 |
出版年 | 102 |
研究生(中文) | 劉恩君 |
研究生(英文) | En-Chun Liu |
學號 | 799190151 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | 英文 |
口試日期 | 2013-06-22 |
論文頁數 | 31頁 |
口試委員 |
指導教授
-
楊國勝
委員 - 李武炎 委員 - 曾貴麟 |
關鍵字(中) |
Hadamard不等式 凸函數 |
關鍵字(英) |
Hadamard's double inequality convex functions |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
設 :I R→R 是一個定義在區間I上的凸函數, I . 則以下不等式成立 (1.1) 此為Hadamard不等式 本文建立一些不等式(1.1)更細緻的結果。 |
英文摘要 |
Let :I R→R be a convex function defined an the interval I of real numbers and I with . Then the following double inequality (1.1) is Hadamard’s inequality. We establish some refinements generalizations of the double inequality(1.1) |
第三語言摘要 | |
論文目次 |
目錄 中文部份 1.緒論 1 2.主要結果 1 參考文獻 15 English part 1.Introduction 17 2. Main Results 17 Reference 30 |
參考文獻 |
[1]. S.S. Dragomir , Two mappings in connection to Hadamard’s inequalities , J. Math. Anal. , 167(1992)49-`56. [2]. S.S. Dragomir and R.P. Agarwal , Two inqualities for differentiable mappings and applications tospecial means of real numbersand 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. , 45(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.va.edu.au/RGMIA/monographs/hermits_hadamard.html] [5]. S.S. Dragomir and S. Wang , A new inequality of Ostrowski’s type in L1 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 , Applications 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. , Hadamard-type inqualities for s-convex functions , Appl. Math. Comp. , 193(2007),26-35. [9]. U.S. Kirmaci , Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula , Appl. Math. Comp. , 147(2004),137-146. [10]. U.S. Kirmaci and M.E. Özdemir , 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. Özdemir , 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 migualities 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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