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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.
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
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Author(s)
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.
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 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
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