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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/51865

    Title: 關於阿達瑪型不等式之研究及其應用
    Other Titles: On some inequalities of Hadamard’s type and applications
    Authors: 許凱程;Hsu, Kai-chen
    Contributors: 淡江大學數學學系博士班
    楊國勝;Yang, Gou-sheng
    Keywords: 赫米提-阿達瑪不等式;費伊爾不等式;凸向函數;梯形公式;Hermite-Hadamard’s inequality;Fejer’s inequality;Convex function;Trapezoidal formula
    Date: 2010
    Issue Date: 2010-09-23 16:13:32 (UTC+8)
    Abstract: 本篇論文共分為五章。第一章中,我們探討赫米提-阿達瑪(Hermite-Hadamard)與費伊爾(Fejér)所提出的不等式如下,令f:[a,b]->R為凸函數,g:[a,b]->R為非負可積分函數且對稱於x=(a+b)/2,則

    In this dissertation, it consists of five chapters. In the first chapter, we introduce Hermite-Hadamard and Fejér inequality. The inequalities are
    where f:[a,b]->R is a convex function and g:[a,b]->R is nonnegative integral function such that g is symmetric to .In the second chapter, there is an introduction of documenting famous Jensen’s inequality and the refinements as well as the generalizations of the Hermite-Hadamard’s inequality which was found by Dragomir, Hong, Milosević, Sándor and Yang, respectively. Furthermore, we give some examples of their proof.
    In the third chapter, we establish some inequalities that are related to the refinements of the Hadamard’s inequality base on Dragomir, Hong, Milosević, Sándor and Yang’s results. In the forth chapter, we establish some inequalities for differentiable convex mappings whose derivatives in absolute value are convex. This results are connected with Fejér’s inequality holding for convex mappings which are generalizations of Dragomir and Agarwal’s results.
    Finally, we discuss its applications to some special means, the weighted trapezoidal formula, r-moment, and the expectation of a symmetric and continuous random variable.
    Appears in Collections:[數學學系暨研究所] 學位論文

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