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Inequalities

Inequalities Acta Applicandae M athematicae 23: (1991) 95 Book Reviews H. G. Hardy, J. E. Littlewood and G. P6lya: Inequalities, 2nd edn., fifth reprint, Cambridge University Press, 1988, xii + 324 pp. $59.50 ($19.95 paperback). The second edition of the book now appears in its fifth unchanged reprint-this convincingly demonstrates the actuality and significance of the book. It is still a standard reference, and in the past it has been cited more than 60 times every year. Clearly, there is not much point in writing a detailed review now when the book has been available to whole generations of analysts and so a few words may suffice. Roughly the contents. The introductional Chapter 1 clarifies the notations and explains some 'methodical' features of the book. Chapters 2-6 give a comprehensive and, in some way, exhaustive treatment of simple inequalities which are 'in daily use' in analysis. This mainly concerns the theorem of the arithmetic and geometric means, H61der's and Minkowski's inequalities and their generalizations (i.e. a more general account of the theory of convex functions). Proofs are given in a variety of ways and the finite, infinite and integral cases of these inequalities are gradually considered. Also, a large number http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Inequalities

Abstract

Acta Applicandae M athematicae 23: (1991) 95 Book Reviews H. G. Hardy, J. E. Littlewood and G. P6lya: Inequalities, 2nd edn., fifth reprint, Cambridge University Press, 1988, xii + 324 pp. $59.50 ($19.95 paperback). The second edition of the book now appears in its fifth unchanged reprint-this convincingly demonstrates the actuality and significance of the book. It is still a standard reference, and in the past it has been cited more than 60 times every year. Clearly, there is not much point...
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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00046921
Publisher site
See Article on Publisher Site

Abstract

Acta Applicandae M athematicae 23: (1991) 95 Book Reviews H. G. Hardy, J. E. Littlewood and G. P6lya: Inequalities, 2nd edn., fifth reprint, Cambridge University Press, 1988, xii + 324 pp. $59.50 ($19.95 paperback). The second edition of the book now appears in its fifth unchanged reprint-this convincingly demonstrates the actuality and significance of the book. It is still a standard reference, and in the past it has been cited more than 60 times every year. Clearly, there is not much point in writing a detailed review now when the book has been available to whole generations of analysts and so a few words may suffice. Roughly the contents. The introductional Chapter 1 clarifies the notations and explains some 'methodical' features of the book. Chapters 2-6 give a comprehensive and, in some way, exhaustive treatment of simple inequalities which are 'in daily use' in analysis. This mainly concerns the theorem of the arithmetic and geometric means, H61der's and Minkowski's inequalities and their generalizations (i.e. a more general account of the theory of convex functions). Proofs are given in a variety of ways and the finite, infinite and integral cases of these inequalities are gradually considered. Also, a large number

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 1, 2004

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