系統識別號 | U0002-2706201217383900 |
---|---|
DOI | 10.6846/TKU.2012.01181 |
論文名稱(中文) | 有關Opial 以及Hermite-Hadamard不等式的推廣與應用 |
論文名稱(英文) | Some Generalizations of Opial’s Inequality, Hermite-Hadamard’s Inequality and applications |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 數學學系博士班 |
系所名稱(英文) | Department of Mathematics |
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 | 100 |
學期 | 2 |
出版年 | 101 |
研究生(中文) | 羅仁傑 |
研究生(英文) | Jen-Chieh Lo |
學號 | 898190011 |
學位類別 | 博士 |
語言別 | 繁體中文 |
第二語言別 | |
口試日期 | 2012-06-15 |
論文頁數 | 80頁 |
口試委員 |
指導教授
-
楊國勝
委員 - 胡德軍 委員 - 劉豐哲 委員 - 高金美 委員 - 張慧京 委員 - 李武炎 委員 - 曾貴麟 委員 - 陳功宇 |
關鍵字(中) |
Opial不等式 時間尺度 赫米提-阿達瑪不等式 凸向函數 |
關鍵字(英) |
Opial’s inequality Time scales Hermite-Hadamard’s inequality Convex function |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
本篇論文共分為四章。第一章中,我們探討Opial所提出的不等式。因為Opial不等式有連續型跟離散型的情形,所以我們希望透過時間尺度(time scales)的觀念將二者結合。 第二章中我們提出了一些Opial不等式在時間尺度上的一些推廣。 第三章中,我們探討赫米提-阿達瑪(Hermite-Hadamard)與費伊爾(Fejer)所提出的不等式。之後並談論一些有關阿達瑪與費伊爾不等式的改善。 最後在第四章中,我們將談論在第三章結果的應用,分別為特殊平均數、隨機變數與加權梯形公式。 |
英文摘要 |
In this dissertation, it consists of four chapters. In the first chapter, we introduce Opial’s inequality.Since there are continuous type and discrete type of Opial inequality, so we hope to combine of both by concept of time scales. In the second chapter, we have some improvement of Opial’s inequalities on time scales. In the third chapter, we introduce Hermite-Hadamard and Fejer inequality. Finally, we discuss its applications to some special means, the weighted trapezoidal formula, r-moment, and the expectation of a symmetric and continuous random variable. |
第三語言摘要 | |
論文目次 |
目錄 第一章 簡介----------------------------------------1 1.1 Opial不等式的介紹------------------------------1 1.2有關連續型Opial不等式的推廣-----------------------1 1.3有關離散型Opial不等式的推廣-----------------------3 1.4有關時間尺度(Time scales)的簡介------------------4 1.5一些在時間尺度上Opial不等式的推廣------------------7 第二章 一些在時間尺度上Opial不等式的改良--------------8 2.1一些在時間尺度上Opial不等式的改良------------------8 2.2一些在時間尺度上Maroni不等式的改良----------------15 第三章 阿達瑪(Hadamard)不等式的介紹-----------------21 3.1 阿達瑪(Hadamard)不等式------------------------21 3.2 一些有關於阿達瑪(Hadamard)不等式的細分-----------22 3.3一些阿達瑪不等式的推廣---------------------------23 第四章 應用---------------------------------------32 參考文獻------------------------------------------36 contents Chapter 1 Introduction---------------------------40 1.1The Introduction of Opial's Inequalities------40 1.2 Some generalizations of Opial's Inequality in Continuous type---------------------------------------------40 1.3 Some generalization of Opial's Inequality in Discrete type---------------------------------------------42 1.4 The Introduction of Time scales--------------43 1.5 Some generalizations of Opial's inequalities on time scales-------------------------------------------46 Chapter 2 Some improvement of Opial's inequalities on time scales-------------------------------------------48 2.1 Some improvement of Opial's inequalities on time scales-----48 2.2 Some improvements of Maroni's inequalities on time scales-55 Chapter 3 Introductions of Hadamard's inequalities-62 3.1 Hadamard’s inequality--------------------------62 3.2 Some refinements of Hadamard’s inequality------63 3.3 Some generalizations of Hadamard's inequalities--------------63 Chapter 4 Applications----------------------------73 References-----------------------------------------77 |
參考文獻 |
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