三角不等式與Jensen不等式之精化; Refinements of triangle inequality and Jensen’s inequality

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:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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