一些與Hadamard不等式相關的反問題

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Title:	一些與Hadamard不等式相關的反問題
Other Titles:	Some inverse problems associated with Hadamard's inequalities
Authors:	高昌平;Gao, Chang-Pian
Contributors:	淡江大學數學學系碩士班陳功宇;Chen, Kung-Yu
Keywords:	阿達瑪不等式;凸性;反問題;Hadamard’s inequalities;convexity;inverse problems
Date:	2017
Issue Date:	2018-08-03 14:47:14 (UTC+8)
Abstract:	設f為開區間I上的連續函數,a∈I。我們定義L_a與P_a如下: L_a (t)≔(f(t)+f(a))/2 (t-a)-∫_a^t〖f(s)ds,a≤t〗。 P_a (t)≔∫_a^tf(s)ds-(t-a)f((t+a)/2),a≤t。我們考慮L_a與P_a的凸性的相關問題及其反問題。 Let f be continuous function in open interval I and a∈I. We define L_a (t)≔(f(t)+f(a))/2 (t-a)-∫_a^t〖f(s)ds,a≤t〗。 P_a (t)≔∫_a^tf(s)ds-(t-a)f((t+a)/2),a≤t。 We study the properties of L_a and P_a.
Appears in Collections:	[Department of Applied Mathematics and Data Science] Thesis

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