Mathematical Inequalities: A Perspective - Hardcover

Cerone, Pietro; Dragomir, Silvestru Sever

Hardcover

ISBN 10: 1439848963 ISBN 13: 9781439848968

Publisher: Chapman and Hall/CRC, 2010

Synopsis

Drawing on the authors’ research work from the last ten years, Mathematical Inequalities: A Perspective gives readers a different viewpoint of the field. It discusses the importance of various mathematical inequalities in contemporary mathematics and how these inequalities are used in different applications, such as scientific modeling.

The authors include numerous classical and recent results that are comprehensible to both experts and general scientists. They describe key inequalities for real or complex numbers and sequences in analysis, including the Abel; the Biernacki, Pidek, and Ryll–Nardzewski; Cebysev’s; the Cauchy–Bunyakovsky–Schwarz; and De Bruijn’s inequalities. They also focus on the role of integral inequalities, such as Hermite–Hadamard inequalities, in modern analysis. In addition, the book covers Schwarz, Bessel, Boas–Bellman, Bombieri, Kurepa, Buzano, Precupanu, Dunkl–William, and Grüss inequalities as well as generalizations of Hermite–Hadamard inequalities for isotonic linear and sublinear functionals.

For each inequality presented, results are complemented with many unique remarks that reveal rich interconnections between the inequalities. These discussions create a natural platform for further research in applications and related fields.

About this title

About the Author:

Pietro Cerone is a professor of mathematics at Victoria University, where he served as head of the School of Computer Science and Mathematics from 2003 to 2008. Dr. Cerone is on the editorial board of a dozen international journals and has published roughly 200 refereed works in the field. His research interests include mathematical modeling, population dynamics, and applications of mathematical inequalities.

Sever S. Dragomir is a professor of mathematics and chair of the international Research Group in Mathematical Inequalities and Applications at Victoria University. Dr. Dragomir is an editorial board member of more than 30 international journals and has published over 600 research articles. His research in pure and applied mathematics encompasses classical mathematical analysis, operator theory, Banach spaces, coding, adaptive quadrature and cubature rules, differential equations, and game theory.

Review:

"Written by two leading experts in this subject, this book is both a text on a topic of current interest in inequalities and a great overview of the techniques and striking applications of the inequalities theory."
--Dumitru Acu, Zentralblatt MATH 1298

"Cerone and Dragomir have successfully produced an extensive list of inequalities used in analysis. ... The writing is straightforward and the text often references results given elsewhere. ... Recommended."
-- J.R. Burke, CHOICE, December 2011

"... a well-written and welcome addition to the literature. ... to have the results in one place is a service to all interested parties."
-- P.S. Bullen, Mathematical Reviews, Issue 2011m

"One of the most interesting aspects is many instances of 'reverses' ... a useful book if you are interested in its specific subject matter ..."
-- MAA Reviews, February 2011

About this edition

• Publisher: Chapman and Hall/CRC
• Publication date: 2010
• ISBN 10: 1439848963
• ISBN 13: 9781439848968
• Binding: Hardcover
• Edition number: 1
• Number of pages: 402