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解析不等式 版权信息
- ISBN:9787519202682
- 条形码:9787519202682 ; 978-7-5192-0268-2
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 所属分类:>>
解析不等式 本书特色
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,该书讲述了许多新的内容,即使在对*经典的不等式的讲述中,也添加了许多新研究。作者力求*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。
解析不等式 内容简介
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,该书讲述了许多新的内容,即使在对*经典的不等式的讲述中,也添加了许多新研究。作者力求*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。
解析不等式 目录
On Notations and Definitions1.Introduction1.1 Real Number System1.1.1 Axioms of the Set of Real Numbers1.1.2 Order Ptoperties of Real Numbcrs1.2 Complex Number System1.3 Monotonc Functions1.4 Convex Functions1.4.1 Definitions of Jensen Convex Functions1.4.2 Continuity of Jenscn Convex Functions1.4.3 Convex Functions1.4.4 Continuity and Differentiability of Convex Functions1.4.5 Logarithmically Convex Functions1.4.6 Some Extensions of the Concept of Convex Functions1.4.7 Hierarchy of Convexity2.General Inequalities2.1 Fundamental Inequalities2.1.1 Simple Means2.1.2 Cauchy's Inequality2.2 Abel's Inequality2.3 Jordan's Inequality2.4 Bemoulli's Inequality and its Generalizations2.5 Cebysev's and Related Inequalities2.6 Cauchy's and Related Inequalities2.6.1 Some Refinements and Extensjons of Cauchy's Inequality2.6.2 Gram's Inequality2.7 Young's Inequality2.8 Holder's Inequality2.9 Minkowski's and Related Inequalities2.10 Inequalities of Aczel, Popoviciu, Kurepa and Bellman2.11 Schweitzer's, Diaz-Metcalf's, Rennie's and Related Inequalities2.12 An Inequality of Fan and Todd2.13 Gross'Inequality2.14 Means2.14.1 Definitions2.14.2 Inequalities Involving Means2.14.3 Ratios and Differences of Means2.14.4 Refinement of the Arithmetic-Geometric Mean Inequality2.14.5 Some General Inequalities Involving Means2.14.6 The λ-Method of Mitrinovic and Vasic2.15 Symmetric Means and Functions2.15.1 Definitions and Main Relations between Symmetric Means2.15.2 Inequalities of Rado-Popoviciu Type2.15.3 Concavity of Certain Functions Involving the Elementary Symmetric Functions2.16 Steffensen's and Related Inequalities2.17 Schur's Inequality2.18 Turan's Inequalities2.19 Benson's Method2.20 Recurrent Inequalities of Redheffer2.21 Cyclic Inequalities2.22 Inequalities Involving Derivatives2.23 Integral Inequalities Involving Derivatives2.23.1 An Inequality Ascribed to Wirtinger2.23.2 An Inequality of Opial2.24 Inequalities Connected with Majorization of Vectors2.25 Inequalities for Vector Norms2.25.1 Triangle Inequality2.25.2 An Identity of Hlawka and the Associated Inequality2.25.3 An Inequality of Hornich2.25.4 Generalizations of Hlawka's Inequality2.25.5 A SteinitzGross Result2.26 Mills Ratio and Some Related Rcsults2.27 Stirling's Formula
3.Particular Inequalities3.1 Inequalities Involving Functions of Discrete Variables3.2 Inequalities Involving Algebraic Functions3.3 Inequalities Involving Polynomials3.4 Incqualities Involving Trigonometric Functions3.5 Inequalities Involving Trigonmetric Polynomials3.6 Inequalities Involving Exponential, Logarithmic and Gamma Functions3.7 Integral Inequalities3.8 Inequalities in the Complex Domain3.9 Miscellaneous InequalitiesName IndexSubject Index
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解析不等式 作者简介
D.S.Mitrinovi?(D.S.米特里诺维奇,塞尔维亚)是国际知名学者,在数学界享有盛誉。本书凝聚了作者多年科研和教学成果,适用于科研工作者、高校教师和研究生。
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