系統識別號 | U0002-1806201508065100 |
---|---|
DOI | 10.6846/TKU.2015.00503 |
論文名稱(中文) | 一些凸函數的不等式的研究 |
論文名稱(英文) | On some inequalities for convex functions |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 數學學系碩士班 |
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 | 103 |
學期 | 2 |
出版年 | 104 |
研究生(中文) | 林琨諭 |
研究生(英文) | Kun-Yu Lin |
學號 | 602190059 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | |
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 |
關鍵字(中) |
厄米阿達碼不等式 凸函數 |
關鍵字(英) |
Hermite-Hadamard inequality convex function |
第三語言關鍵字 | |
學科別分類 | |
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. |
第三語言摘要 | |
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 [1] S.S. Dragomir, Two mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl., 167(1992)49-56. [2] S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbersand to trapezoidal formula, Appl. Math. Lett., 11(1998)91-95. [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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