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中文論文名稱 關於 Hermite-Hadamard不等式一些更細緻的結果
英文論文名稱 Some Refinements of Hermite-Hadamard Inequalities
校院名稱 淡江大學
系所名稱(中) 中等學校教師在職進修數學教學碩士學位班
系所名稱(英) Executive Master's Program In Mathematics for Teachers
學年度 102
學期 2
出版年 103
研究生中文姓名 李孟儒
研究生英文姓名 Meng-Ju Lee
學號 701190059
學位類別 碩士
語文別 中文
第二語文別 英文
口試日期 2014-06-17
論文頁數 54頁
口試委員 指導教授-楊國勝
委員-李武炎
委員-曾貴麟
中文關鍵字 Hadamard's不等式  Hermite-Hadamard's不等式  凸函數 
英文關鍵字 Hadamard's inequalities  Hermite-Hadamard's inequalities  convex 
學科別分類
中文摘要 設f是一個定義在區間I的凸實數函數,其中a,b屬於I,而且a小於b,那麼下面的Hadamard's不等式成立
這個雙重不等式稱為Hermite-Hadamard's不等式(或Hadamard's不等式)。
本文的主要目的是針對Hadamard's不等式的做一些推廣和建立一些更細緻的結果。
英文摘要 Let f be a convex real-valued function defined on an interval I of real numbers (a,b) and with a small then b. Then the Hadamard’s inequalities hold. This double inequality is known in the literature as the Hermite-Hadamard’s (or Hadamard’s) inequality.
The main purpose of this paper is to give some generalizations and refinements of the Hadamard’s inequality.
論文目次 目錄

中文部分

1.引言 1

2.準備工作 1

3.主要結果 6

參考文獻 26

English part

1. Introduction 28

2. Preliminary 28

3. Main Results 33
Reference 53
參考文獻 References

[1] R.P. Angarwal ans S.S. Dragomir, An application of Hayashi's inequality for differentiable function, Computers Math. Applic. 32 (6) (1996), 95-99.

[2] M.Alomari, M. Darus ans S.S. Dragomir, New inequalities of Hermite-Hadamard type for functions where second derivative absolute values are quasi-convex, Tamkang, J. Math. Vol 41 No.4 (2010), 353-359.

[3] M. Alomari, M. Darus and U.S. Kirmaci, Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Comp.Math. Appl., 59 (2010), 225-232.

[4] S.S. Dragomir and R.P. Angarwal, Two mapping in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.

[5] S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95.

[6] S.S. Dragomir, Y.J. Cho and S.S. Kim, Inequalities of Hadamard's type for Lipschitzian mappings and their applicaitions, J. Math. Anal. Appl., 245 (2000), 489-501.

[7] A. Florea and C.P. Niculescu, A Hermite-Hadamard inequalityn for convex-concave symmetric functions, Bull. Soc. Sci. Math. Roum., 50 (98) (2007), No. 2, 149-156.

[8] J.Hadamard, Etude sur les proprieties des fonctions entieres et en particulier d'une function consideree par Riemann, J. Math. Pures et Appl. 59 (1893), 171-215.

[9] Ch. Hermite, Sur deux limites d'une integrale definie, Mathesis 3 (1883), 82.

[10] D.A.Ion, Some estimates on the Hermite-Hadamard inequality through quasi-conver functions, Annals of University of Craiova. Math. Comp. Sci. Ser., 34 (2004), 82-87.

[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. Ozdemir, On some inequalities ofr differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp., 153 (2004), 361-368.

[13] M. Mihailescu and C.P. Niculescu, An extension of the Hermite-Hadamard inequality through subharmonic functions, Glasgow Mathematical Jourmal 49 (2007), 1-6.

[14] D.S. Mitrinović, J.E. Pečarić and A.M. Fink, Inequalities Involving Functions and Theit Integrals and Decivatives, K'LUWER ACADEMIC PUBLISHERS, DORDRECHT/BOSTON/LONDOW, 1991.

[15] C.P. Niculescu and L.-E. Persson, Convex Functions and ther Applications. A Contemporaty Approach, CMS Books in Mathematics vol. 23, Springer-Verlag, New York, 2006.

[16] M.E. Ozdemir, A theorem on mappings with bounded derivatives with applications to quadrature rules and means, Appl. Math. Comp., 138 (2000), 425-434.

[17] 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/hermite-hadamard.html.

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

[19] G.S. Yang, D.Y. Hwang and K.L. Tseng, Some inequalilies for differentiable convex and concave mappings, Appl. Math. Comp., 47 (2004), 207-216.
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