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| 系統識別號 |
U0002-1206201209574600 |
| 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
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| 學科別分類 |
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| 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
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| 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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| 論文使用權限 |
同意紙本無償授權給館內讀者為學術之目的重製使用，於2012-06-18公開。同意授權瀏覽/列印電子全文服務，於2012-06-18起公開。 |
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