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  • 解析不等式(英文版)
    該商品所屬分類:自然科學 -> 數學
    【市場價】
    611-884
    【優惠價】
    382-553
    【介質】 book
    【ISBN】9787519202682
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    內容介紹



    • 出版社:世界圖書出版公司
    • ISBN:9787519202682
    • 作者:(塞爾維亞)米特裡諾維奇
    • 頁數:400
    • 出版日期:2016-03-01
    • 印刷日期:2016-03-01
    • 包裝:平裝
    • 開本:24開
    • 版次:1
    • 印次:1
    • 字數:336千字
    • 今天不等式在數學領域發揮著顯著的作用,而且
      已經形成了一個非常活躍、引人注目的研究領域。與
      之前的研究不等式的書相比,米特裡諾維奇所著的《
      解析不等式(英文版)》講述了許多新的內容,即使
      在對最經典的不等式的講述中,也添加了許多新研究
      。作者力求最大限度的詳盡,而且給出了盡可能多的
      相關參考資料。目次:引言;普通不等式;特殊不等
      式;人名索引;主題索引。
    • On Notations and Definitions
      1.Introduction
      1.1 Real Number System
      1.1.1 Axioms of the Set of Real Numbers
      1.1.2 Order Ptoperties of Real Numbcrs
      1.2 Complex Number System
      1.3 Monotonc Functions
      1.4 Convex Functions
      1.4.1 Definitions of Jensen Convex Functions
      1.4.2 Continuity of Jenscn Convex Functions
      1.4.3 Convex Functions
      1.4.4 Continuity and Differentiability of Convex Functions
      1.4.5 Logarithmically Convex Functions
      1.4.6 Some Extensions of the Concept of Convex Functions
      1.4.7 Hierarchy of Convexity
      2.General Inequalities
      2.1 Fundamental Inequalities
      2.1.1 Simple Means
      2.1.2 Cauchy's Inequality
      2.2 Abel's Inequality
      2.3 Jordan's Inequality
      2.4 Bemoulli's Inequality and its Generalizations
      2.5 Cebysev's and Related Inequalities
      2.6 Cauchy's and Related Inequalities
      2.6.1 Some Refinements and Extensjons of Cauchy's Inequality
      2.6.2 Gram's Inequality
      2.7 Young's Inequality
      2.8 Holder's Inequality
      2.9 Minkowski's and Related Inequalities
      2.10 Inequalities of Aczel, Popoviciu, Kurepa and Bellman
      2.11 Schweitzer's, Diaz-Metcalf's, Rennie's and Related Inequalities
      2.12 An Inequality of Fan and Todd
      2.13 Gross'Inequality
      2.14 Means
      2.14.1 Definitions
      2.14.2 Inequalities Involving Means
      2.14.3 Ratios and Differences of Means
      2.14.4 Refinement of the Arithmetic-Geometric Mean Inequality
      2.14.5 Some General Inequalities Involving Means
      2.14.6 The λ-Method of Mitrinovic and Vasic
      2.15 Symmetric Means and Functions
      2.15.1 Definitions and Main Relations between Symmetric Means
      2.15.2 Inequalities of Rado-Popoviciu Type
      2.15.3 Concavity of Certain Functions Involving the Elementary Symmetric Functions
      2.16 Steffensen's and Related Inequalities
      2.17 Schur's Inequality
      2.18 Turan's Inequalities
      2.19 Benson's Method
      2.20 Recurrent Inequalities of Redheffer
      2.21 Cyclic Inequalities
      2.22 Inequalities Involving Derivatives
      2.23 Integral Inequalities Involving Derivatives
      2.23.1 An Inequality Ascribed to Wirtinger
      2.23.2 An Inequality of Opial
      2.24 Inequalities Connected with Majorization of Vectors
      2.25 Inequalities for Vector Norms
      2.25.1 Triangle Inequality
      2.25.2 An Identity of Hlawka and the Associated Inequality
      2.25.3 An Inequality of Hornich
      2.25.4 Generalizations of Hlawka's Inequality
      2.25.5 A SteinitzGross Result
      2.26 Mills Ratio and Some Related Rcsults
      2.27 Stirling's Formula
      3.Particular Inequalities
      3.1 Inequalities Involving Functions of Discrete Variables
      3.2 Inequalities Involving Algebraic Functions
      3.3 Inequalities Involving Polynomials
      3.4 Incqualities Involving Trigonometric Functions
      3.5 Inequalities Involving Trigonometric Polynomials
      3.6 Inequalities Involving Exponential, Logarithmic and Gamma Functions
      3.7 Integral Inequalities
      3.8 Inequalities in the Complex Domain
      3.9 Miscellaneous Inequalities
      Name Index
      Subject Index
     
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