2nd Edition

Dictionary of Inequalities

By Peter Bullen Copyright 2015
    405 Pages
    by Chapman & Hall

    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.

    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

    Biography

    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.

    "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 Čebišev). 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 Mitrinović 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