English  |  正體中文  |  简体中文  |  Items with full text/Total items : 66984/66984 (100%) Visitors : 22964270      Online Users : 403
 Scope All of NCUIR 理學院    數學研究所       --博碩士論文 Tips: please add "double quotation mark" for query phrases to get precise resultsplease goto advance search for comprehansive author search Adv. Search
 NCU Institutional Repository > 理學院 > 數學研究所 > 博碩士論文 >  Item 987654321/7917

 Please use this identifier to cite or link to this item: `http://ir.lib.ncu.edu.tw/handle/987654321/7917`

 Title: 三角不等式與Jensen不等式之精化;Refinements of triangle inequality and Jensen’s inequality Authors: 許至勇;Chih-Yung Hsu Contributors: 數學研究所 Keywords: 三角不等式;triangle inequality;Jensen’s inequality Date: 2007-07-04 Issue Date: 2009-09-22 11:09:01 (UTC+8) Publisher: 國立中央大學圖書館 Abstract: 在這篇論文中，我們對於一個在Banach空間中的可積分向量值函數，證明了此函數具有 sharp triangle inequality 並且也證明了其三角不等式的reverse inequality， 這之中亦涵蓋了對於 n 個元素的特例，此特例是由 Kato 等學者所發表過的一個結果。此外我們也對一個在LP空間中的向量值函數,推廣了它另一種形式的三角不等式，我們的結果包含了對於兩個元素的特例。另外關於一個改良過的Jensen’s inequality 我們亦討論了其一些相關的性質。 In this thesis, we prove a sharp triangle inequality and its reverse inequality for strongly integrable functions with values in a Banach space X. This contains as a special case a recent result of Kato et al on sharp triangle inequality for n elements. We also discuss a generalized triangle inequality for Lp functions with values in X. It contains as a special case the triangle inequality of the second kind for two elements, which is implied by the Euler-Lagrange type identity. Besides, some properties related to a refined Jensen’s inequality are observed. Appears in Collections: [數學研究所] 博碩士論文

Files in This Item:

File SizeFormat
0KbUnknown732View/Open