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中文論文名稱 準凸函數的 Hermite-Hadamerd 型不等式的研究
英文論文名稱 Some Inequalities of Hermite-Hadamerd’s type for quasi-convex functions
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 100
學期 2
出版年 101
研究生中文姓名 蔡黃凱
研究生英文姓名 Huang-Kai Tsai
學號 799190086
學位類別 碩士
語文別 中文
第二語文別 英文
口試日期 2012-06-09
論文頁數 44頁
口試委員 指導教授-楊國勝
委員-李武炎
委員-胡德軍
中文關鍵字 Hermite-Hadamard 不等式  準凸函數 
英文關鍵字 Hermite-Hadamard inequality  Quasi-convex function. 
學科別分類
中文摘要 Hermite-Hadamerd’s不等式是相當多人研究的不等式,本研究主要欲建立 Hermite-Hadamard 之右邊不等式,其中所討論的函數,其導數之絕對值為準凸函數。
英文摘要 The main purpose of this paper is to establish inequalities related to the right hand side of Hermite-Hadamard’s type for function whose derivatives in absolute value are quasi-convex .
論文目次 中文摘要 i
英文摘要 ii
目 次 iii
一、 前言 1
二、 主要的結果 4
參考文獻 21
附錄
1. Introduction 23
2. Main results 26
References 43
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 numbers and 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 S. Wang , A new inequality of Ostrowski’s type in norm
and applications to some special means and for some numerical quadrature rule ,
Tamkang J. Math , 28(1997) , 239-244 .
[5] 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) ,105-109 .
[6] D.A. Ion, Some estimates on the Hermite-Hadamard inequality through
quasi-convex functions , Annals of University of Craiova , Math. Comp. Sci.
Ser. , 34(2007) , 82-87 .
[7] 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.
[8] 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 .
[9] M.E. Ozdemir , Atheorem on mappings with bounded derivatives with
applications to quadrature rules and means, Appl. Math . Comp, 138(2003) ,
425-434
[10] C.E.M. Pearce and J. Pecaric , Inequalities for differectiable mappings with
application to special means , Appl. Math. Comp. 13(2000) , 51-55.
[11] G.S. Yang , D.Y. Hwang and K.I.. Tseng , Some inequalities for differentiable
convex and concave mappings , Comp. Math. Appl. , 47(2004), 207-216.
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