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A dictionary of inequalities. (English) Zbl 0934.26003
Pitman Monographs and Surveys in Pure and Applied Mathematics. 97. Harlow: Longman. x, 283 p. $ 86.95; £52.00 (1998).

This book is a reference book which contains many inequalities. They can be located either by name or by subject. The scope of the book is broad: the classical inequalities for various means, inequalities of Hardy, Landau, Kolmogorov, Sobolev, Bernstein, Markov, Hadamard, and many other inequalities are formulated. Proofs are not included but references are given.

The bibliography contains references to many books published on inequalities, but relatively few references to papers. Although the material covered is very large, the book does not cover all inequalities known. Many geometrical inequalities are not discussed, the book by Yu. D. Burago and V. A. Zalgaller: “Geometric inequalities” (Russian) (1980; Zbl 0436.52009; English translation 1988; Zbl 0633.53002), is not mentioned. Inequalities for eigenvalues of differential and abstract operators are basically not discussed. One may find other omissions, but on the other hand it is probably impossible to cover completely such a diverse and vast area as inequalities.

The book is a useful addition to the literature.


MSC:
26DxxInequalities involving real functions
00A20Dictionaries and other general reference works