解析不等式

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