系統識別號 | U0002-2606200723573000 |
---|---|
DOI | 10.6846/TKU.2007.00844 |
論文名稱(中文) | 應用梯形法則於 Čebyšev不等式的研究 |
論文名稱(英文) | A note on Čebyšev type inequalities via Trapezoidal-Like rules |
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 | 95 |
學期 | 2 |
出版年 | 96 |
研究生(中文) | 朱建豪 |
研究生(英文) | Jian-Hau Ju |
學號 | 693150152 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | |
口試日期 | 2007-05-30 |
論文頁數 | 28頁 |
口試委員 |
指導教授
-
楊國勝
委員 - 王忠信(wangcs@email.au.edu.tw) 委員 - 胡德軍 委員 - 楊國勝 |
關鍵字(中) |
Čebyšev不等式 梯形法則 絕對連續函數 可微函數 等式 |
關鍵字(英) |
Čebyšev type inequalities Trapezoid-like rules Absolutely continuous functions Differentiable functions Identities |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
在本文中,我們建立和 Čebyšev 積分不等式相似的新的不等式包含了函數和它們根據某些梯形法則的導數。 |
英文摘要 |
In this paper we establish new inequalities similar to the Čebyšev integral inequality involving functions and their derivatives via certain Trapezoidal like rules |
第三語言摘要 | |
論文目次 |
目錄 1.導論………………………………………………..P1 2.主要結論…………………………………………..P2 定理2.1……………………………………………P2 定理2.2……………………………………………P4 定理2.3……………………………………………P7 定理2.4……………………………………………P10 3.參考文獻…………………………………………P13 Contents 1.Introduction……………………………………………P15 2.Main results……………………………………………P16 Theorem2.1………………………………………………P16 Theorem2.2………………………………………………P18 Theorem2.3………………………………………………P21 Theorem2.4………………………………………………P24 3.References……………………………………………….P28 |
參考文獻 |
[1] N.S. BARNETT AND S.S. DRAGOMIR, On the perturbed trapezoid formula, Tamkang J. Math, 33(2) (2002), 119-128 [2] P.L. CEBYSEV , Sur les expressions approximatives des limites, Proc. Math. Soc. Charkov, 2 (1882), 93-98 [3] S.S. DRAGOMIR AND S. MABIZELA, Some error estimates in trapezoidal quadrature rule, RGMIA Res. Rep. Coll.,2(5)(1999), 653-663.[ONLINE: http://rgmia.vu.edu.au/v2n5.html] [4] S.S. DRAGOMIR, J.SUNDE AND C. BUSE, Some new inequalities for Jeffreys divergence measure in information theory, RGMIA Res. Rep. Coll.,3(2) (2000), 235-243 [ONLINE: http://rgmia.vu.edu.au/v3n2.html] [5] H.P. HEINIG AND L. MALIGRANDA, Chebyshev inequality in function spaces, Real Analysis and Exchange, 17(1991-92), 211-247 [6] D.S. MITRINOVIC , J.E. PECARIC AND A.M. FINK, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993 [7] B.G. PACHPATTE, On trapezoid and Gruss like integral inequalities, Tamkang J. Math., 34(4) (2003), 365-369 [8] B.G. PACHPATTE, New weighted multivariate Gruss type inequalities, J. Inequal.Pure and Appl. Math., 4(5) (2003), Art. 108 [ONLINE: http://rgmia.vu.edu.au/article.php?sid=349] [9] B.G. PACHPATTE, New Čebyšev type inequalities via Trapezoidal-Like rules, J. Inequal.Pure and Appl. Math., 7(1) , Art. 31, 2006,1-6 [10] B.G. PACHPATTE, A note on Chebychev –Gruss type inequalities for differentiable functions, Tamusi Oxford J. Math Sci., to appear. [11] J.E. PECARIC, F. PORCHAN AND Y. TONG, Convex Functions, Partial Ordering. and Statistical Applications, Academic Press, San Diego, 1992 |
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