Sedrakyan H., Sedrakyan N. Algebraic Inequalities

Springer, 2018. — 244 p. — (Problem Books in Mathematics). — ISBN: 3319778358.This unique collection of new and classical problems provides full coverage of algebraic inequalities. Many of the exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. Algebraic Inequalities can be considered a continuation of the book Geometric Inequalities: Methods of Proving by the authors.
This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving algebraic inequalities.Basic Inequalities and Their Applications
Sturm’s Method
The HM-GM-AM-QM Inequalities
The Cauchy–Bunyakovsky–Schwarz Inequality
Change of Variables Method
Using Symmetry and Homogeneity
The Principle of Mathematical Induction
A Useful Inequality
Using Derivatives and Integrals
Using Functions
Jensen’s Inequality
Inequalities of Sequences
Algebraic Inequalities in Number Theory
Miscellaneous Inequalities