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研究生:羅裕豪
研究生(外文):Yu-Hao Lo
論文名稱:一些Ostrowski不等式的推廣
論文名稱(外文):Some Generalizations of Ostrowski Inequality
指導教授:陳功宇
指導教授(外文):Kung-Yu Chen
口試委員:楊國勝曾貴麟
口試委員(外文):Gou-Sheng YangKuei-Lin Tseng
口試日期:2017-07-19
學位類別:碩士
校院名稱:淡江大學
系所名稱:數學學系碩士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:21
中文關鍵詞:Ostrowski不等式
外文關鍵詞:Ostrowski Inequality
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在這篇論文我們建立了一些Ostrowski型態的不等式,推廣並改良前人所做的一些結果。
In this paper, we establish some inequalities which improve some Ostrowski type inequalities.
第一章:導論………………………………………………………………1
1.1:已建立的Ostrowski不等式
1.2:由Dragomir, Tseng, Yang跟Chou所建立的結果
第二章:一些加權的Ostrowski不等式的改良……………………………7

參考文獻…………………………………………………………………20
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 rules, Tamkang J. of Math., 28(1997), 239-244
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 rules, Appl. Math. Lett., 11(1) (1998), 105-109
S. S Dragomir and S. Wang, An new inequality of Ostrowski’s type in L_p [a ,b]-norm, Indian J. Math. 40(3)(1998), 299-304
S. S Dragomir, The Ostrowski integral inequality for mappings of bounded variation, Bull. Australian Math. Soc., 60(1999), 495-508
S. S Dragomir, Ostrowski’s inequality for monotonous mappings and applications, J. KSIAM 3(1)(1999), 127-135
S. S Dragomir, The Ostrowski’s integral inequality for Lipschitzian mappings and applications,Comput. Math. Appl. ,38(1999), 33-37
S. S Dragomir,A new generalization Ostrowski’s integral inequality for mappings whose derivatives are bounded and applications in numberical integration and for special means,Appl. Math. Lett.,13 (2000), 19-25
S. S Dragomir,On the Ostrowski’s integral inequality for mappings with bounded variation and applications,Math. Inequal. Apple.,4(1)(2001), 59-66
S. S Dragomir, A generalization of Ostrowski’s integral inequality for mappings whose derivatives belong to L_p [a ,b] and applications in numberical integration,J. Math. Anal. Appl.,255(2001), 605-626
S. S Dragomir, A generalization of Ostrowski’s integral inequality for mappings whose derivatives belong to L_1 [a ,b] and applications in numberical integration,J. Comput. Anal. Appl.,3(4)(2001), 343-360
S. S Dragomir, A generalization of Ostrowski’s integral inequality for mappings whose derivatives belong to L_∞ [a ,b] and applications in numberical integration,J. KSIAM.,5(2)(2001), 117-136
D. S. Mitrinovi''c, J.E. Peµcari''c and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers(Dordrecht), 1994.
A. Ostrowski, üeber die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv., 10 (1938), 226-227
H. L. Royden, Real Analysis Third Edition, Macmillan Publishing Company,1988
Kuei-Lin Tseng, Shiow-Ru Hwang, S. S Dragomir, Generalizations of weighted Ostrowski type inequality for mappings of bounded variation and their applications, Comput. Math.Appl.,55(8)(2008), 1785-1793
Kuei-Lin Tseng, Improvements of some inequality of Ostrowski type and their applications, Taiwanese J. Math.,12(9)(2008), 2427-2441
Kuei-Lin Tseng,Shiow-Ru Hwang,Gou-Sheng Yang,Yi-Ming Chou,Improvements of the Ostrowski integral inequality for mappings of bounded variation I,Appl. Math. Comp. ,217(8)(2010)2348-2355
Kuei-Lin Tseng,Shiow-Ru Hwang,Gou-Sheng Yang,Yi-Ming Chou,Weighted Ostrowski integral inequality for mappings of bounded variation,Taiwanese J. Math.,15(2)(2011)573-585
周義銘, 在有界變分函數上有關Ostrowski型之不等式研究。淡江大學數學學系博士班學位論文。2012。1-99
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