Dictionary of Inequalities: 2nd Edition (Hardback) book cover

Dictionary of Inequalities

2nd Edition

By Peter Bullen

Chapman and Hall/CRC

405 pages

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pub: 2015-06-15
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Description

Adding new results that have appeared in the last 15 years, Dictionary of Inequalities, Second Edition provides an easy way for researchers to locate an inequality by name or subject. This edition offers an up-to-date, alphabetical listing of each inequality with a short statement of the result, some comments, references to related inequalities, and sources of information on proofs and other details. The book does not include proofs and uses basic mathematical terminology as much as possible, enabling readers to access a result or inequality effortlessly.

New to the Second Edition

  • More than 100 new inequalities, including recently discovered ones
  • Updated inequalities according to the most recent research
  • Inclusion of a name index
  • Updated bibliography that contains URLs for important references

The book mainly presents the most common version of the inequality and later gives more general results as extensions or variants. Inequalities that exist at various levels of generality are presented in the simplest form with the other forms as extensions or under a different heading. The author also clarifies any non-standard notations and includes cross-references for transliterations.

Reviews

"This second edition by Bullen (emer., Univ. of British Columbia) contains new results, corrections, and an up-to-date bibliography of sources, including websites with URLs. The inequalities are categorized by the name of the original author (e.g., Cauchy's Inequality), the type of inequality (e.g., Norm Inequalities), or both; entries are listed in alphabetical order. In cases where an author's name may have several accepted spellings, the multiple spellings are represented (e.g., looking up Tchebysheff directs one to the entry for Cebišev). Rather than providing proofs for each inequality, the author gives a list of related inequalities contained in the book as well as a list of references for further reading. The work is clearly intended for researchers but contains information also accessible to advanced undergraduates. That being said, it is entertaining to explore the suggested related inequalities and see where they lead. The author notes the deliberate omission of historic developments, elementary geometric identities, and all but a few number theoretic inequalities, a decision he bases in part on the existence of monographs addressing each topic (e.g., citing a number of the works available in English and Serbian by mathematician Dragoslav Mitrinovic and colleagues). Summing up: Recommended. Upper-level undergraduates through faculty/researchers; professional mathematicians."

—J. R. Burke, Gonzaga University, Spokane, Washington, USA, for CHOICE, March 2016

Table of Contents

Introduction

Notations

Abel–Arithmetic

Backward–Bushell

Čakalov–Cyclic

Davies–Dunkl

Efron–Extended

Factorial–Furuta

Gabriel–Guha

Haber–Hyperbolic

Incomplete–Iyengar

Jackson-Jordan

Kaczmarz–Ky Fan

Labelle–Lyons

Mahajan–Myers

Nanjundiah–Number

Operator–Ōzeki

Pachpatte–Ptolemy

Q-Class–Quaternion

Rademacher–Rotation

Saffari–Székely

Talenti–Turán

Ultraspherical–von Neumann

Wagner–Wright

Yao–Zeta

Bibliography

Name Index

Index

About the Author

Peter Bullen is a professor emeritus in the Department of Mathematics at the University of British Columbia. Dr. Bullen is a member of the Canadian Mathematical Society, the American Mathematical Society, and the Mathematical Association of America. His research focuses on real analysis, including non-absolute integrals and inequalities.

About the Series

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
SCI055000
SCIENCE / Physics
TEC009000
TECHNOLOGY & ENGINEERING / Engineering (General)