數個函數乘積之積分不等式之研究

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Thesis > Item 987654321/32910

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Title:	數個函數乘積之積分不等式之研究
Other Titles:	Integral inequalities involving the product of several functions
Authors:	許凱程;Hsu, Kai-chen
Contributors:	淡江大學數學學系碩士班楊國勝;Yang, Gou-sheng
Keywords:	積分不等式;數個函數乘積;離散模式;等式;Integral inequalities;Product of several functions;Discrete analogues;Identities
Date:	2007
Issue Date:	2010-01-11 02:57:59 (UTC+8)
Abstract:	在本篇論文中，建立數個函數乘積之積分不等式的一般性結果及離散模式。一般性結果： \|product_{i=1}^{n}f_{i}(x)-[sum_{i=1}^{n}w_{i}F_{i}(product_{j eq i}f_{j}(x))]\| leq M[sum_{i=1}^{n}w_{i}(integral_{a}^{b}\|f_{i}^{''}(t)\|dt)\|product_{j eq i}f_{j}(x)\|] (1) 離散模式： \|product_{i=0}^{m}u_{i,j}-sum_{i=0}^{m}gamma _{i}(product_{l eq i}u_{l,j})U_{i}\| leq M{sum_{i=0}^{m}[gamma_{i}\|product_{l eq i}u_{l,j}\|(sum_{j=0}^{n-1}\|Delta u_{i,j}\|)]} (2) 上式(1)與(2)用以估計數個函數乘積及離散模式的偏差。 We establish the general results of integral inequalities involving the product of several functions and their derivatives. The discrete analogues of the main results are also given. The product of several functions: \|product_{i=1}^{n}f_{i}(x)-[sum_{i=1}^{n}w_{i}F_{i}(product_{j eq i}f_{j}(x))]\| leq M[sum_{i=1}^{n}w_{i}(integral_{a}^{b}\|f_{i}^{''}(t)\|dt)\|product_{j eq i}f_{j}(x)\|] (1) The discrete analogues: \|product_{i=0}^{m}u_{i,j}-sum_{i=0}^{m}gamma _{i}(product_{l eq i}u_{l,j})U_{i}\| leq M{sum_{i=0}^{m}[gamma_{i}\|product_{l eq i}u_{l,j}\|(sum_{j=0}^{n-1}\|Delta u_{i,j}\|)]} (2) The above inequalities (1) and (2) can be used to estimate the deviation of the product of several functions. The discrete versions of the main results are also given.
Appears in Collections:	[Graduate Institute & Department of Mathematics] Thesis

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