## An introduction to inequalities |

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### Contents

Note to the Reader vii | 3 |

Absolute Value | 25 |

The Classical Inequalities | 47 |

Copyright | |

4 other sections not shown

### Common terms and phrases

absolute value algebraic am/n arithmetic mean Arithmetic-Mean arithmetic-mean-geometric-mean inequality Axiom bm/n calculus Cauchy inequality Chapter city-block distance consider coordinates curve d(OP d(OQ d(OR defined definition denote determine Dido's Problem distance function ellipse ellipsoid equality holds equation equivalent Euclidean distance Exercise expression Figure foregoing formula geometric mean geometric-mean inequality given harmonic mean Hence Holder inequality inequality 3.6 isosceles line segment mathematical induction Minkowski inequality multiplying negative number non-Euclidean length nonnegative numbers nonnegative quantities nonnegative values nth roots obtain origin perimeter plane point set positive integers positive numbers proof properties proved rational numbers rectangular box relationship result right-hand root-mean-square satisfying shown in Fig sides sign of equality Sketch the graph slope solution symbol symmetric with respect Theorem 4.1 theory of inequalities three nonnegative tive number triangle inequality 4.50 unit circle unit disc xi,yi yields zero