Secrets in Inequalities - basic inequalities

It is true that there are very many books on inequalities and you have all the right to be bored and tired of them. But we tell you that this is not the case with this one. Just read the proof of Nesbitt's Inequality in the very beginning of the material, and you will understand exactly what we mean.Every topic is described through various and numerous examples taken from many sources, especially from math contests around the world, from recent contests and recent books, of from (more or less) specialized sites on the Internet, which makes the book very lively and interesting to read for those who are involved in such activities, students and teachers from all over the world.Don't let the problems overwhelm you, though they are quite impressive problems, study applications of the first five basic inequalities mentioned above, plus the Abel formula, symmetric inequalities and the derivative method. Now relax with the AM-GM inequality - the foundational brick of inequalities. Cuprins PrefaceAcknowledgementsAbbreviations and NotationsI The basic Inequalities1 AM-GM nequality1.1 AM-GM Inequality and Applications1.2 The Cauchy Reverse Technique2 Cauchy-Schwarz and Holder inequalities2.1 Cauchy-Schwarz inequality and Applications2.2 Holder Inequality3 Chebyshev Inequality3.1 Chebyshev Inequality and Applications3.2 The Chebyshev Associate Technique4 Inequalities with Convex Functions4.1 Convex functions and Jensen inequality4.2 Convex Functions and Inequalities with Variables Restricted to an Interval5 Abel Formula and Rearrangement Inequality5.1 Abel formula5.2 Rearrangement Inequality6 The Method of Balanced Coefficients6.1 Balancing coefficients by AM-GM inequality6.2 Balancing coefficients by Cauchy-Schwarz and Holder inequalities7 Derivative and Applications7.1 Derivative of one-variable functions7.2 Derivative of n-Variable Functions8 A note on symmetric inequalities8.1 Getting started8.2 Primary symmetric polynomials8.3 Normalization skill8.4 Symmetric separation9 Problems and SolutionsGlossary