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.
Table of Contents
Discrete Inequalities. Integral Inequalities for Convex Functions. Ostrowski and Trapezoid-Type Inequalities. Grüss-Type Inequalities and Related Results. Inequalities in Inner Product Spaces. Inequalities in Normed Linear Spaces and for Functionals. References. Index.
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.