English  |  正體中文  |  简体中文  |  Items with full text/Total items : 51756/86971 (60%)
Visitors : 8356477      Online Users : 103
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library & TKU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/110901


    Title: Some refinements of hermite-hadamard inequality
    Other Titles: 一些更精緻的 Hermite-Hadamard 不等式
    Authors: 郭妙霓;Guo, Miao-Ni
    Contributors: 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
    Keywords: Hermite-Hadamard 不等式;凸函數;Hermite-Hadamard inequality;convex functions.
    Date: 2016
    Issue Date: 2017-08-24 23:38:54 (UTC+8)
    Abstract: 本文中均假設 I = [a, b],f為I上的函數:
    若f : I → ℝ為I中的凸函數,則
    f((a+b)/2)≤1/(b-a)∫_a^b▒〖f(x)dx≤(f(a)+f(b))/2 〗, (1.1)
    恆成立,為眾所週知的Hermite-Hadamard不等式。
    若f為I中的凸函數,是否存在實數 l 及L 滿足下列不等式:
    f((a+b)/2)≤l≤1/(b-a)∫_a^b▒〖f(x)dx≤L≤(f(a)+f(b))/2〗, (1.2)
    本論文研究的主要目的,是為了提供問題 (1.2)更多的答案。
    Throughout, let I denote the closed interval [a, b] of real numbers.
    If f : I → ℝ is convex on I, then
    f((a+b)/2)≤1/(b-a)∫_a^b▒〖f(x)dx≤(f(a)+f(b))/2.〗 (1.1)
    This is the classical Hermite-Hadamard inequality.
    If f is a convex function on I, do there exist real numbers l, L
    such that
    f((a+b)/2)≤l≤1/(b-a)∫_a^b▒〖f(x)dx≤L≤(f(a)+f(b))/2.〗 (1.2)
    The main purpose of this paper is to give more answers to the question (1.2).
    Appears in Collections:[數學學系暨研究所] 學位論文

    Files in This Item:

    File Description SizeFormat
    index.html0KbHTML31View/Open

    All items in 機構典藏 are protected by copyright, with all rights reserved.


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