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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