臺灣博碩士論文加值系統

在這篇論文之中，我們主要的結果是推廣Ostrowski型不等式。我們首先介紹一些定義及相關的性質。Ostrowski 提出一個不等式﹝見定理1.1式﹞，此不等式很廣泛的被應用。
在這篇論文之中，我們主要以Ostrowski type這個式子為主﹝見定理1.1式﹞，並加以推廣﹝見引理2.1、定理2.2、定理2.3、定理2.4及定理2.5﹞。
在這篇論文之中，定理2.3是最主要被推導出來的結果，若f(x)函數在n-1次微分之後，在[a,b]區間上為絕對連續函數，則對所有x在[a,b]區間裡，我們會得到三個重要的不等式。
在定理2.4中，若f(x)函數在n次微分之後，在[a,b]區間上為有界變分函數，則對所有x在[a,b]區間裡，我們會得到﹝2.6﹞這一個不等式。
在定理2.5中，若f(x)函數在n-1次微分之後，在[a,b]區間上為單調非遞減且n次微分之後導數存在的函數，則對所有x在[a,b]區間裡，我們會得到﹝2.7﹞這一個不等式。
最後推導出其一般的形式；當n = 1代入一般式時，我們會得到原本的Ostrowski 不等式

In this paper, we established some generalizations of Ostrowski Type Inequality.
The authors first introduce some definitions and properties. Ostrowski proposes an
inequality (theorem 1.1) that is applied widely.
In this paper, I make Ostrowski type as a main inequality and derive it. ( see Lemma2.1, Theorem2.2, Theorem2.3,Theorem2.4 and Theorem2.5.)
Theorem2.3 is the main result in this paper. If the (n-1)-th derivative of f(x) is absolutely continuous on [a,b], then for all x belongs to [a,b], we have three important inequalities.
In Theorem2.4, if the n-th derivative of f(x) is of bounded variation on [a,b], then for all x belongs to [a,b], we have an inequality (2.6).
In Theorem2.5, if the (n-1)-th derivative of f(x) is monotonic nondecreasing and the n-th derivative of f(x) exists on [a,b], then for all x belongs to [a,b], we have an inequality (2.7).
Finally it can be derived as a normal form that when n=1, we can get the original
Ostrowski inequality.

目錄
1.介紹…………………………………………………………………… 1
定理1.1……………………………………………………………………1
定理1.2……………………………………………………………………2
定理1.3……………………………………………………………………3
定理1.4……………………………………………………………………3
2.主要結論……………………………………………………………… 4
引理2.1……………………………………………………………………4
定理2.2……………………………………………………………………4
定理2.3……………………………………………………………………5
定理2.4……………………………………………………………………8
定理2.5……………………………………………………………………9
3.參考文獻………………………………………………………………11
contents 1. Introduction……………………………………………………… 12
Theorem 1.1…………………………………………………………… 12
Theorem 1.2…………………………………………………………… 13
Theorem 1.3…………………………………………………………… 14
Theorem 1.4…………………………………………………………… 14
2. Main results……………………………………………………… 15
Lemma 2.1……………………………………………………………… 15
Theorem 2.2…………………………………………………………… 15
Theorem 2.3………………………………………………………… 16
Theorem 2.4…………………………………………………………… 19
Theorem 2.5…………………………………………………………… 20
3.References……………………………………………………………22

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