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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 ¦Ë-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