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系統識別號 |
U0002-1806201508065100 |
中文論文名稱
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一些凸函數的不等式的研究 |
英文論文名稱
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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
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中文關鍵字 |
厄米阿達碼不等式 
凸函數 
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英文關鍵字 |
Hermite-Hadamard inequality 
convex function 
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學科別分類 |
學科別>自然科學>數學
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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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