Inequalities

1. The Fundamental Inequalities and Related Matters.- § 1. Introduction.- § 2. The Cauchy Inequality.- § 3. The Lagrange Identity.- § 4. The Arithmetic-mean - Geometric-mean Inequality.- § 5. Induction - Forward and Backward.- § 6. Calculus and Lagrange Multipliers.- § 7. Functional Equations.- § 8. Concavity.- § 9. Majorization - The Proof of Bohr.- § 10. The Proof of Hurwitz.- § 11. A Proof of Ehlers.- § 12. The Arithmetic-geometric Mean of Gauss; the Elementary Symmetric Functions.- § 13. A Proof of Jacobsthal.- § 14. A Fundamental Relationship.- § 15. Young's Inequality.- § 16. The Means Mt (x, ?) and the Sums St(x).- § 17. The Inequalities of Hölder and Minkowski.- § 18. Extensions of the Classical Inequalities.- § 19. Quasi Linearization.- § 20. Minkowski's Inequality.- § 21. Another Inequality of Minkowski.- § 22. Minkowski's Inequality for 0