Art of Solving Problems, 2015. - 154 с.The first four volumes of this book are a great opportunity to see and know many old and new elementary methods for solving: (1) symmetric polynomial inequalities (in real variables and nonnegative real variables); (2) symmetric rational inequalities; (3) symmetric nonrational inequalities; (4) cyclic and noncyclic inequalities. The last volumes, starting with Volume 5, contain new beautiful original methods for creating and solving discrete inequalities using half convex function method, partially convex function method for Jensen’s type inequalities, HCF and PCF methods for inequalities with ordered variables, equal variable method for nonnegative or real variables, arithmetic compensation method, the highest coefficient cancellation method for symmetric homogeneous polynomial inequalities of degree six, seven and eight in nonnegative or real variables, methods involving either strong or necessary and sufficient conditions for cyclic homogeneous inequalities of degree four in real or nonnegative variables and so on.Half Convex Function Method.
Theoretical Basis.
Application.
Solutions.
Partially Convex Function Method.
Theoretical Basis.
Application.
Solutions.
Half Convex Function Method for Ordered Variables.
Theoretical Basis.
Application.
Solutions.
Partially Convex Function Method for Ordered Variables.
Theoretical Basis.
Application.
Solutions.
Equal Variable Method for Nonnegative Variables.
Theoretical Basis.
Application.
Solutions.
Equal Variable Method for Real Variables.
Theoretical Basis.
Application.
Solutions.
Arithmetic Compensation Method.
Theoretical Basis.
Application.
Solutions.
Cyclic Homogeneous Polynomial Inequalities in Real Variables.
Theoretical Basis.
Application.
Solutions.
Cyclic Homogeneous Polynomial Inequalities in Nonnegative Variables.
Theoretical Basis.
Application.
Solutions.
Symmetric Homogeneous Polynomial Inequalities in Real Variables.
Theoretical Basis.
Application.
Solutions.
Symmetric Homogeneous Polynomial Inequalities in Nonnegative Variables.
Theoretical Basis.
Application.
Solutions.
Best Upper Bound of Jensen’s Difference.
Theoretical Basis.
Application.
Solutions.
