Discrete Inequalities of the Cauchy Bunyakovsky Schwartz Type

This book is a rather long (almost exhaustive) list of inequalities of the Cauchy Bunyakovsky Schwartz (CBS) Type, as well as related inequalities. Because the literature dedicated to inequalities is very rich, it very appropriate that each chapter in the book is followed by a bibliography. In short: anybody interested to learn about discrete inequalities (student, teacher, or researcher) will find abundant material in this book.

Each chapter in the book has a long list of theorems, most of them followed by proofs and bibliographical references. While such an approach is mathematically correct, it is somewhat arid, mostly because there isn't much insight into the thought process behind the proofs (some of which are quite technical). The reviewer noticed also a few typos; they could very easily be fixed.

The book is very informative and self-contained. As an example, we will note that less known concepts are treated in extensive sections, divided into a few sub-sections:

• 5.6 A Weighted Version of Ozeki's Inequality is the title of a section with five sub-sections;
• 5.7 Extensions of the Gruss Inequality has three sub-sections, the last one, 5.7.3 Applications to Ozeki's Inequality, making the connection with the previous section.

Although there are many books and articles on inequalities, Dragomir's book is certainly one that should be checked out by a reader interested in learning or applying discrete inequalities.