Classical and new inequalities in analysis. (English) Zbl 0771.26009

Mitrinović, D. S.; Pečarić, J. E.; Fink, A. M.

Mathematics and Its Applications. East European Series. 61. Dordrecht: Kluwer Academic Publishers. xvii, 740 p. (1993).

This is an excellent book that seems to prove that there is no possibility of a last word on inequalities. Most of the topics have been treated in other recent books, but there is still much that is new. The book is very well organised and so everything is easy to find; an important point in a book that will be a reference for users of inequalities. Each chapter is devoted to a specific inequality, groups of inequalities or methods of proof; Bernoulli’s inequality, Hölder’s inequality, Norm inequalities, Cyclic inequalities, The centroid method, Quasilinearization methods, for instance. In addition to the latest information on each topic there is usually a full and authorative historical account. While there is no index the nature of the organization of the book makes this not too important; there is a full list of cited authors. In many cases proofs are omitted but since each chapter is provided with its own bibliography the source of the proof is easy to find.
All in all this is a book that everyone working with inequalities should have. There are some infelicities in English usage but none that get in the way of understanding. No serious errors were found, and the typesetting is a great improvement on that in an earlier book on inequalities in this series.

Reviewer: P.S.Bullen (Vancouver)

MSC:

26Dxx	Inequalities in real analysis
26D15	Inequalities for sums, series and integrals
26-02	Research exposition (monographs, survey articles) pertaining to real functions

Keywords:

inequalities; means