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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/105295


    Title: 一些凸函數的不等式的研究
    Other Titles: On some inequalities for convex functions
    Authors: 林琨諭;Lin, Kun-Yu
    Contributors: 淡江大學數學學系碩士班
    楊國勝
    Keywords: 厄米阿達碼不等式;凸函數;Hermite-Hadamard inequality;Convex function
    Date: 2015
    Issue Date: 2016-01-22 14:52:33 (UTC+8)
    Abstract: 若f,g:[a,b]→[0,∞) 在 [a,b] 是凸函數,Pachpatte建立了以下的定理:1/(b-a)((∫_a^b)f(x)g(x)dx))≤1/3M(a,b)+1/6N(a,b)其中 M(a,b)=f(a)g(a)+f(b)g(b) 且 N(a,b)=f(a)g(b)+f(b)g(a).本文的主要目的,是要建立一些較此不等式更細緻化的不等式。
    If f,g:[a,b]→[0,∞) are convex functions on [a,b],Pachpatte proved the following:1/(b-a)((∫_a^b)f(x)g(x)dx))≤1/3M(a,b)+1/6N(a,b),where M(a,b)=f(a)g(a)+f(b)g(b) and N(a,b)=f(a)g(b)+f(b)g(a).We give in this paper several refinements of the above inequality.
    Appears in Collections:[數學學系暨研究所] 學位論文

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