淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-2606201320180800
中文論文名稱 準凸函數的Hermite-Hadamard's 不等式及其 在一些平均數的應用
英文論文名稱 Hermite-Hadamard's inequalities for quasi-convex functions and applications to special mean of real numbers
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 101
學期 2
出版年 102
研究生中文姓名 曾泓予
研究生英文姓名 Hong-Yu Tseng
學號 700190142
學位類別 碩士
語文別 中文
口試日期 2013-06-20
論文頁數 30頁
口試委員 指導教授-楊國勝
委員-楊國勝
委員-張慧京
委員-曾貴麟
中文關鍵字 凸函數  準凸函數  不等式 
英文關鍵字 convex  quasi-convex  Hermite-Hadamard inequality 
學科別分類
中文摘要 這篇論文當中, 我們建立了一些準凸函數的Hermite-Hadamard型的不等式, 以及一些在平均數上的應用。
英文摘要 In the present paper,we establish several inequalities of Hermite-Hadamard type for functions of quasi-convex.
論文目次 中文部份
1.序論...............................1
2.本文...............................3
3.特殊平均數的應用...................8
參考文獻............. ...............12
English part
1.Introduction.......................15
2.Main Results ......................18
3. Applications To Special Means ... 24
References ......................... 28
參考文獻 [1] M.Alomari, M. Darus and 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.
[2] R.P. Agarwal and S.S Dragomir, An application of Hayashi’s inequality for differentiable function, Computers Math. Applic. 32 (6) (1996), 95-99.
[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] M. Alomari and M. Darus, Some Ostrowski type inequalities for quasi-convex functions with applications to special means, RGMIA, 13 (2) (2010), article No.3.
Preprint.
[5] M. Alomari and M. Darus, On the Hadamard’s inequality for log-convex functions on the coordinates, J. Ineq. Appl. Volume 2009, Article ID 283147, 13 pages doi:10.1155/2009/283147.
[6] M. Alomari and M. Darus, On some inequalities Simpson-type via quasi-convex functions with applications, Trans. J. Math. Mech. (TJMM), (2) (2010), 15-24.
[7] M. Alomari, M. Darus and Dranomir, Inequalities of Hermite-Hadamard’s type for functions whose derivatives absolute values are quasi-convex, Punjab University J.
Math. submitted.
[8] S. S. Dragomir, Two mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.
[9] 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.
[10] 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.
[11] S. S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in L1 norm and
applications to some special means and to some numerical quadrature rule, Tamkang J. Math., 28 (1997) , 239-244.
[12] S. S. Dragomir and S. Wang, An inequality of Ostrowski-Gruss type and its applications to the estimation of error bounds for some special means and for some
numerical quadrature rule, Computers Math. Applic. 33 (11) (1997), 15-20.
[13] S. S. Dragomir , On some inequalities for differentiable convex functions and applications, (submitted).
[14] A. Florea and C. P. Niculescu, A Hermite-Hadamard inequality for convex-concave symmetric functions, Bull. Soc. Sci. Math. Roum., 50 (98) (2007), No. 2, 149-156.
[15] I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, Elsevier Inc. 7ed., 2007.
[16] J. Hadamard, Etude sur les proprieties des fonctions entieres et en particulier d’une function consideree par Riemann, J. Math. Pures et Appl. 58 (1893), 171-215.
[17] Ch. Hermite, Sur deux limites d’une integrale definie, Mathesis 3 (1883), 82.
[18] 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.
[19] 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.
[20] U. S. Kirmaci and M. E. Ozdemir, 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.
[21] M. Mihailescu and C. P. Niculescu, An extension of the Hermite-Hadamard inequality through subharmonic functions, Glasgow Mathematical Journal 49 (2007), 1-6.
[22] D.S. Mitrinovi′c, J.E. Peˇcari′c and A.M. Fink, Inequalities Involving Functions and Theit Integrals and Derivatives, K’LUWER ACADEMIC PUBLISHERS,
DORDRECHT/BOSTON/LONDOW,1991.
[23] C. P. Niculescu and L.-E. Persson, Old and New on the Hermite-Hadamard Inequality Real Anal Exchange, 29 (2003/2004), 663-686. [24] C. P. Niculescu and L.-E. Persson, Convex Functions and their Applications. A
Contemporary Approach, CMS Books in Mathematics vol. 23, Springer-Verlag, New York, 2006.
[25] M. E. Ozdemir, A theorem on mappings with bounded derivatives with applications to quadrature rules and means, Appl. Math. Comp., 138 (2000), 425-434.
[26] 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.
[27] C. E. M. Pearce and J.E. Peˇcari′c, Inequalilies for differentiable mappings with application to special means and quadrature formula, Appl. Math Lett., 13 (2000),
51-55.
[28] 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.
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2013-07-02公開。
  • 同意授權瀏覽/列印電子全文服務,於2013-07-02起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信