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Titlu: Algebraic Inequalities

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The name of Vasile Cirtoaje, in mathematical terms, actually equals with inequalities. Many problems from the book, their majority I would say, are obtained by the author himself. If you will carefully read the book, you may find that your skills in solving inequalities were considerably improved. However, one needs not to read every single page of this material; the chapters are independent and you may even open the book somewhere, arbitrarily, and try to solve an inequality or find its solution from the book. Also, we must add that the book is full of up to date problems, since the author is an active member of the Mathlinks Site Forum on the Internet. Last, but not least, one has to remark the outstanding tenacity and enthusiasm of the author in solving inequalities; definitely, he is a passionate of this realm of elementary mathematics. And this book is neither more, nor less than a work of a master.

Marian Tetiva


1. Warm-up problem set
1.1 Applications
1.2 Solutions

2. Starting from some special fourth degree inequalities
2.1 Main results
2.2 Solutions
2.3 Another related inequalities
2.4 Solutions

3. Inequalities with right convex and left concave functions
3.1 Inequalities with right convex functions
3.2 Inequalities with left concave functions
3.3 Inequalities with left concave-right convex functions
3.4 Applications
3.5 Solutions

4. On Popoviciu's inequality
4.1 Introduction
4.2 Applications
4.3 Solutions

5. Inequalities involving EV-Theorem
5.1 Statement of results
5.2 Applications
5.3 Solutions

6. Arithmetic/Geometric Compensation Method
6.1 Arithmetic Compensation Method
6.2 Geometric Compensation Method
6.3 Applications
6.4 Solutions

7. Symmetric inequalities with three variables involving fractions
7.1 Inequalities involving E1
7.2 Solutions
7.3 Inequalities involving E2
7.3 Solutions
7.5 Inequalities involving E1 and E2
7.6 Solutions
7.7 Other related inequalities
7.8 Solutions

8. Final problem set
8.1 Applications
8.2 Solutions


List of Symbols and Glossary

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