| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 許至勇 | zh_TW |
| DC.creator | Chih-Yung Hsu | en_US |
| dc.date.accessioned | 2007-7-7T07:39:07Z | |
| dc.date.available | 2007-7-7T07:39:07Z | |
| dc.date.issued | 2007 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=942201015 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.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。 | zh_TW |
| dc.description.abstract | 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. | en_US |
| DC.subject | 三角不等式 | zh_TW |
| DC.subject | triangle inequality | en_US |
| DC.subject | Jensen’s inequality | en_US |
| DC.title | 三角不等式與Jensen不等式之精化 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | Refinements of triangle inequality and Jensen’s inequality | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |