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中文論文名稱 可微函數的一些不等式及其某些平均數的應用
英文論文名稱 Ineqalities for Differentiable Mapping and Applications to Special means of Real numbers
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 100
學期 2
出版年 101
研究生中文姓名 蘇明慧
研究生英文姓名 Ming-Hui Sue
學號 799190094
學位類別 碩士
語文別 中文
第二語文別 英文
口試日期 2012-06-07
論文頁數 37頁
口試委員 指導教授-楊國勝
委員-張慧京
委員-曾貴麟
中文關鍵字 不等式 
英文關鍵字 Hermite-Hadamard inequality 
學科別分類
中文摘要 函數在區間上是凸函數,就是我們在所熟知關於凸函數的Hermite-Hadamard 不等式 [3,P49]。
在參考文獻[7] Dragomir 及 Agarwal証明了以下的引理。
這份論文的目的是為了要推廣定理B和定理C,並且應用他們在一些特殊的平均數和不規則四邊形的公式上。
英文摘要 Let f be a convex function on the interval of real numbers and with aFor several recent results concerning Hermite-Hadamard’s inequality, we refer the interested reader to [1-6], where further references are listed.
In [7] Dragomir and Agarwal proved the following lemma.
The aim of this paper is to give some generalizations of theorem B and theorem C as well as to apply them to some special means and to trapezoidal formula..
論文目次 目 次
中文摘要 i
英文摘要 ii
目 次 iii
第壹章 前言 1
第貳章 主要結果 2
第參章 特殊平均數的應用 6
第肆章 梯形公式的應用 13
參考文獻 17
Content
1.Introduction 19
2. Main results 20
3.Application to special means 24
4.Application to trapezoidal formula 32
References 37
參考文獻 1.J. E. Pacaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Ordering and Applications, Academic Press, New York, (1991)
2.S. S.Dragomir, J. E. Pacaric, and J. Sandor, A note on the Jensen-Hadamard’s inequality, And. Num. Ther. Approx. 19, 29-34 (1990).
3.S. S. Dragomir, Two mappings in connection to Hadamard’s inequality, J Math. Anal. Appl. 167, 49-56(1992).
4.S. S. Dragomir, On Hadamard’s inequalities, for convex functions, Mat. Balkanica 6, 215-222(1992).
5.S. S. Dragomir and C. Buse, Refinements of Hadamard’s inequality for multiple integrals, Utilitias Math. 47, 193-198(1995).
6.S. S. Dragomir, J. E. Pacaric and L. E Pesaso, Some inequalities of Hadamard type, Soochow J. Math. 21, 335-341(1995).
7.S. S. Dragomir and R. P. Agarwal, Two Inqualities for differentiable Mapings and Aplications to Special Means of Real Number and to Trapezoid Formula, Appl. Math. Leff. Vol II N0.5 91-95 (1998)
8.R. P. Agarwal and S. S. Dragomir, An application of Hayashi’s inequality for differentiable functions, Computers Math. Applic. 32(6),95-99(1996).
9.S. S. Dragomir and S. Wang, Applications of Ostrowaki’s inequality to the estimation of error bounds for some special means and for some numerical quadrature rule, Appl. Math. Lett.11(1), 105-109(1998).
10.S. S. Dragomir and S. Wang, An inequality of Ostrowaki’-Griiss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rule, Computers Math. Applic. 33(11),15-20(1997).
11.S. S. Dragomir and S. Wang, A new inequality of Ostrowaki’s type in norm and applications to some special means and to some numerical quadrature rule,amkang J. Math. (to appear).
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