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Inequalities

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Table of Contents

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    Book Overview
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    Chapter 1 Basic (Elementary) Inequalities and Their Application
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    Chapter 2 Inequalities Between Means (with Two and Three Variables)
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    Chapter 3 Geometric (Triangle) Inequalities
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    Chapter 4 Bernoulli’s Inequality, the Cauchy–Schwarz Inequality, Chebishev’s Inequality, Surányi’s Inequality
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    Chapter 5 Inequalities Between Means (General Case)
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    Chapter 6 The Rearrangement Inequality
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    Chapter 7 Convexity, Jensen’s Inequality
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    Chapter 8 Trigonometric Substitutions and Their Application for Proving Algebraic Inequalities
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    Chapter 9 Hölder’s Inequality, Minkowski’s Inequality and Their Variants
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    Chapter 10 Generalizations of the Cauchy–Schwarz Inequality, Chebishev’s Inequality and the Mean Inequalities
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    Chapter 11 Newton’s Inequality, Maclaurin’s Inequality
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    Chapter 12 Schur’s Inequality, Muirhead’s Inequality and Karamata’s Inequality
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    Chapter 13 Two Theorems from Differential Calculus, and Their Applications for Proving Inequalities
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    Chapter 14 One Method of Proving Symmetric Inequalities with Three Variables
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    Chapter 15 Method for Proving Symmetric Inequalities with Three Variables Defined on the Set of Real Numbers
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    Chapter 16 Abstract Concreteness Method (ABC Method)
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    Chapter 17 Sum of Squares (SOS Method)
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    Chapter 18 Strong Mixing Variables Method (SMV Theorem)
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    Chapter 19 Method of Lagrange Multipliers
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    Chapter 20 Problems
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    Chapter 21 Solutions
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