一些與凸函數相關的多重積分序列

淡江大學機構典藏 > 理學院 > 應用數學與數據科學學系 > 學位論文 > Item 987654321/114270

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Title:	一些與凸函數相關的多重積分序列
Other Titles:	Some sequences of multiple integral associated with convex functions
Authors:	莊逸丞;Chuang, Yi-Cheng
Contributors:	淡江大學數學學系碩士班陳功宇;Chen, Kung-Yu
Keywords:	Jensen不等式;凸函數;多重積分序列;Jensen’s inequality;convex functions;Sequences of multiple integral
Date:	2017
Issue Date:	2018-08-03 14:47:10 (UTC+8)
Abstract:	令 f∶I⊆R→R 是有界的Lebesgue可積函數，g∶[a,b]→I 是一個連續函數，且對所有 n∈N，{q_i (n)∶1≤i≤n} 是一個正實數序列。我們定義下列序列： A_n (f,g;q)∶= 1/(b-a)^n ∫_([a,b]^n)f((q_1 (n)g(x_1 )+⋯+q_n (n)g(x_n ))/Q_n ) dx，這裡 Q_n∶=∑_(i=1)^n〖q_i (n) 〗，dx=dx_1⋯dx_n 。　　我們探討序列 A_n (f,g;q)的收斂及估計。 Let f∶I⊆R→R be a bounded Lebesgue integrable function, g∶[a,b]→I be continuous function, and for each n∈N, {q_i (n)∶1≤i≤n} is a sequence of positive real numbers. We define the sequence: A_n (f,g;q)∶= 1/(b-a)^n ∫_([a,b]^n)f((q_1 (n)g(x_1 )+⋯+q_n (n)g(x_n ))/Q_n ) dx， where Q_n=∑_(i=1)^n〖q_i (n) 〗, dx=dx_1⋯dx_n. We investigate the properties of convergence and estimation of the sequence A_n (f,g;q).
Appears in Collections:	[應用數學與數據科學學系] 學位論文

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