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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
參考文獻 參考文獻
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[3] S.S. Dragomir, Y.J. Cho and S.S. Kim, Inequalities of Hadamard’s type for Lipschitzian mappings and their applications, J. Math. Anal. Appl., 245(2000), 489-501.

[4] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000. Online: [http://www.Staff.vu.edu.au/RGMIA/monographs/hermits_hadamard.html]

[5] S.S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in L_1 norm and applications to some special means and to some numerical quadrature rule, Tamkang J. Math., 28(1997)239-244.

[6] S.S. Dragomir and S. Wang, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and for some numerical quadrature rule, Appl. Math. Lett., 11(1998)1005-109.

[7] J. Hadamard, Etude Sur les proprieties des functions entieres etenparticuller du ́ne function considerre par Riemann, J. Math. Pures et Appl. 59(1893)171-215.

[8] Ch. Hermite, Sur deux limites du ́ne integral define, Mathsis 3(1883), 82.

[9] H. Hudzik and L. Maligraanda, Some remarks on s-convex functions, Aequations Math., 48(1994), 100-111.

[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.

[15] C.E.M. Pearce and J. Pec ̌acic ́, Inequalities for differentiable mappings with application to special means and quadrature formula, Appl. Math. Lett., 13(2000)51-55.

[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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