Pham Kim Hung. Secrets in Inequalities. Volume 1

Table of contents.
preface.
Acknowledgements.
Abbreviations and Notations.
the basic Inequalities.
AM-GM Inequality.
AM-GM Inequality and Applications.
the Cauchy Reverse Technique.
Cauchy-Schwarz and Holder inequalities.
Cauchy-Schwarz inequality and Applications.
Holder Inequality.
Chebyshev Inequality.
Chebyshev Inequality and Applications.
The Chebyshev Associate Technique.
nequalities with Convex Functions.
Convex functions and Jensen inequality.
Convex Functions and Inequalities with Variables Restricted to an.
nterval.
Abel Formula and Rearrangement Inequality.
Abel formula.
Rearrangement Inequality.
The Method of Balanced Coefficients.
Balancing coefficients by AM-GM inequality.
Balancing coefficients by Cauchy-Schwarz and Holder inequalities.
Derivative and Applications.
Derivative of one-variable functions.
Derivative of n-Variable Functions.
A note on symmetric inequalities.
Getting started.
Primary symmetric polynomials.
Normalization skill.
Symmetric separation.
Problems and Solutions.
Glossary.