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| 系統識別號 |
U0002-1806201508065100 |
| 中文論文名稱
|
一些凸函數的不等式的研究 |
| 英文論文名稱
|
On some inequalities for convex functions |
| 校院名稱 |
淡江大學 |
| 系所名稱(中) |
數學學系碩士班 |
| 系所名稱(英) |
Department of Mathematics |
| 學年度 |
103 |
| 學期 |
2 |
| 出版年 |
104 |
| 研究生中文姓名 |
林琨諭 |
| 研究生英文姓名 |
Kun-Yu Lin |
| 學號 |
602190059 |
| 學位類別 |
碩士 |
| 語文別 |
中文 |
| 口試日期 |
2015-06-16 |
| 論文頁數 |
28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 |
厄米阿達碼不等式
凸函數
|
| 英文關鍵字 |
Hermite-Hadamard inequality
convex function
|
| 學科別分類 |
學科別＞自然科學＞數學
|
| 中文摘要 |
若f，g：[a,b]→[0,∞) 在 [a,b] 是凸函數，Pachpatte建立了以下的定理：1/(b-a)((∫_a^b)f(x)g(x)dx))≤1/3M(a,b)+1/6N(a,b)其中 M(a,b)=f(a)g(a)+f(b)g(b) 且 N(a,b)=f(a)g(b)+f(b)g(a).本文的主要目的，是要建立一些較此不等式更細緻化的不等式。 |
| 英文摘要 |
If f，g：[a,b]→[0,∞) are convex functions on [a,b],Pachpatte proved the following:1/(b-a)((∫_a^b)f(x)g(x)dx))≤1/3M(a,b)+1/6N(a,b),where M(a,b)=f(a)g(a)+f(b)g(b) and N(a,b)=f(a)g(b)+f(b)g(a).We give in this paper several refinements of the above inequality. |
| 論文目次 |
目錄
一些凸函數的不等式的研究 1
簡介 1
主要結果 1
參考文獻 27
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| 參考文獻 |
參考文獻
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[10] U.S. Kirmaci et al. Hadamard-type inequalities for s-convex functions, Appl. Math. Comp., 193(2007), 26-35.
[11] 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.
[12] U.S. Kirmaci and M.E. O ̈zdemir, 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.
[13] M.E. O ̈zdemir, A theorem on mappings with bounded derivatives with applications to quadrature rules and means, Appl. Math. Comp., 138(2003)425-434.
[14] B.G. Pachpatte, On some inequalities for convex functions RGMIA Res/Coll. 6 (E)(2003), http://rgmia.vu.edu.au/v6(E).html.
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[16] 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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| 論文使用權限 |
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