【假一罚四】解析不等式(英文版)
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作者(塞尔维亚)米特里诺维奇
出版社世界图书出版公司
ISBN9787519202682
出版时间2016-03
装帧其他
开本其他
定价65元
货号3570988
上书时间2024-12-24
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目录
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
内容摘要
今天不等式在数学领域发挥着显著的作用，而且已经形成了一个非常活跃、引人注目的研究领域。与之前的研究不等式的书相比，米特里诺维奇所著的《解析不等式（英文版）》讲述了许多新的内容，即使在对最经典的不等式的讲述中，也添加了许多新研究。作者力求最大限度的详尽，而且给出了尽可能多的相关参考资料。目次：引言；普通不等式；特殊不等式；人名索引；主题索引。
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