淡江大學機構典藏:Item 987654321/74166
English  |  正體中文  |  简体中文  |  全文筆數/總筆數 : 62797/95867 (66%)
造訪人次 : 3733790      線上人數 : 378
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library & TKU Library IR team.
搜尋範圍 查詢小技巧:
  • 您可在西文檢索詞彙前後加上"雙引號",以獲取較精準的檢索結果
  • 若欲以作者姓名搜尋,建議至進階搜尋限定作者欄位,可獲得較完整資料
  • 進階搜尋
    請使用永久網址來引用或連結此文件: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/74166


    題名: On hermite-hadamard type inequalities for functions whose derivatives are s-convex in the second sense
    其他題名: 有關導數為第二類s-凸函數的Hermite-Hadamard不等式的研究
    作者: 洪秋月;Hung, Chiu-Yueh
    貢獻者: 淡江大學中等學校教師在職進修數學教學碩士學位班
    楊國勝;Yang, Gou-Sheng
    關鍵詞: 凸函數;s-凸函數;Hadamard不等式;convex;s-convex;Hadamard’s inequality
    日期: 2011
    上傳時間: 2011-12-28 18:12:43 (UTC+8)
    摘要: 對所有凸函數 ,則下列不等式恆成立
    . (1.1)
    即稱為Hadamard不等式。
    我們注意到J. Hadamard不是第一個發現此不等式。正如D.S. Mitrinović和 I.B. Lačković所指出,C.Hermite比J. Hadamard早就在10年前於1883年就發現此不等式。
    Hudzik 和 Mailgranda 研究另一型態的s-凸函數,並稱為第二類s-凸函數,這種類型的函數定義如下: 對一些固定實數 而言,若函數 滿足對所有 和 [0,1],下列不等式恆成立:

    則此函數稱為第二類s-凸函數,記作 。
    當 時,可輕易發現 s-凸函數變成定義域在 的一般凸函數。
    由Pearce and Pečarić和Kirmaci et al.所證出的定理是計算(1.1)式的中間項和右項的差。而這篇論文的主要研究目的則是探討(1.1)式的中間項和左項的差。
    The following inequalities
    . (1.1)
    which hold for all convex mappings are known in the literature as Hadamard’s inequality. We note that J. Hadamard was not the first who discovered them. As is pointed out by D.S. Mitrinović and I.B. Lačković, the inequalities (1.1) are due to C.Hermite who obtained them in 1883, ten years before J. Hadamard.
    Hudzik and Mailgranda considered, among others, the class of functions which are s-convex in the second sense. This class is defined in the following way: a function is said to be s-convex in the second sense if

    holds for all , [0,1] and for some fixed . The class of s-convex functions in the second sense is denoted by .
    It is easily seen that for , s-convexity reduces to the ordinary convexity of functions defined on .
    The theorems which were proved by Pearce and Pečarić and Kirmaci et al. are estimating the difference between the middle and right terms in (1.1). The aim of this paper is estimating the difference between the middle and left terms in (1.1).
    顯示於類別:[數學學系暨研究所] 學位論文

    文件中的檔案:

    檔案 大小格式瀏覽次數
    index.html0KbHTML204檢視/開啟

    在機構典藏中所有的資料項目都受到原著作權保護.

    TAIR相關文章

    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library & TKU Library IR teams. Copyright ©   - 回饋