Handbook of Means and Their Inequalities / Edition 2

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Overview

This is a revision of an earlier work "Means and Their Inequalities" by the present author and Professors Mitrinovic and Vasic. Not only does this book bring the earlier version up to date but enlarges the scope considerably to give a full and in-depth treatment of all aspects of the field. While the mention of means occurs in many books this is the only full treatment of the subject. Outstanding features of the book are the variety of proofs given for many of the basic results, over seventy for the inequality between the arithmetic and geometric means for instance, an exhaustive bibliography and a list of mathematicians who have contributed to this field from the time of Euclid to the present day.

This book is written in a language that not only the expert on the subject will understand and appreciate, but graduate students worldwide as well. Any person with an interest in means and then inequalities should find this book within their comprehension although to fully appreciate all the topics covered a knowledge of calculus and of elementary real analysis is required.

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Editorial Reviews

From the Publisher
"This book is indeed a handbook: it is hard to find a subfield of inequalities related to means that is not described in detail, or at least referred to. It is written in a language that can be understood not only by experts but also by graduate students and others who are interested in the applications: the only requirement on readers is a knowledge of calculus and elementary real analysis."—MATHEMATICAL REVIEWS
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Product Details

  • ISBN-13: 9781402015229
  • Publisher: Springer Netherlands
  • Publication date: 12/31/1987
  • Series: Mathematics and Its Applications (closed) Series , #560
  • Edition description: 2nd ed. 2003
  • Edition number: 2
  • Pages: 538
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.25 (d)

Table of Contents

Preface to "Means and their Inequalities"
Preface to the Handbook
Basic References
Notations
A List of Symbols
An Introductory Survey
Ch. I Introduction 1
Ch. II The Arithmetic, Geometric and Harmonic Means 60
Ch. III The Power Means 175
Ch. IV Quasi-Arithmetic Means 266
Ch. V Symmetric Polynomial Means 321
Ch. VI Other Topics 368
Bibliography 439
Name Index 511
Index 525
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