Advances In Mathematical Inequalities
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| Author | : Shigeru Furuichi |
| Publisher | : |
| Total Pages | : 230 |
| Release | : 2020-02-13 |
| Genre | : |
| ISBN | : 9783110643435 |
Mathematical inequalities are essential tools in mathematics, natural science and engineering. This book gives an overview on recent advances. Some generalizations and improvements for the classical and well-known inequalities are described which will are applied and further developed in many fields. Applications of the inequalities to entropy theory and quantum physics are also included.
| Author | : Praveen Agarwal |
| Publisher | : Springer |
| Total Pages | : 351 |
| Release | : 2018-12-31 |
| Genre | : Mathematics |
| ISBN | : 9811330131 |
This book is a collection of original research and survey articles on mathematical inequalities and their numerous applications in diverse areas of mathematics and engineering. It includes chapters on convexity and related concepts; inequalities for mean values, sums, functions, operators, functionals, integrals and their applications in various branches of mathematics and related sciences; fractional integral inequalities; and weighted type integral inequalities. It also presents their wide applications in biomathematics, boundary value problems, mechanics, queuing models, scattering, and geomechanics in a concise, but easily understandable way that makes the further ramifications and future directions clear. The broad scope and high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers. All the contributing authors are leading international academics, scientists, researchers and scholars.
| Author | : Dragoslav S. Mitrinovic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 728 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 9401578427 |
| Author | : B. G. Pachpatte |
| Publisher | : Elsevier |
| Total Pages | : 606 |
| Release | : 2005-05-04 |
| Genre | : Mathematics |
| ISBN | : 0080459390 |
The book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics.* It contains a variety of inequalities which find numerous applications in various branches of mathematics.* It contains many inequalities which have only recently appeared in the literature and cannot yet be found in other books.* It will be a valuable reference for someone requiring a result about inequalities for use in some applications in various other branches of mathematics.* Each chapter ends with some miscellaneous inequalities for futher study.* The work will be of interest to researchers working both in pure and applied mathematics, and it could also be used as the text for an advanced graduate course.
| Author | : George A. Anastassiou |
| Publisher | : World Scientific |
| Total Pages | : 423 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9814317624 |
This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end. The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and HardyOpial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as ChebyshevGruss, Gruss and Comparison of Means inequalities are studied. The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.
| Author | : Mohammad Bagher Ghaemi |
| Publisher | : Springer Nature |
| Total Pages | : 287 |
| Release | : 2021-07-11 |
| Genre | : Mathematics |
| ISBN | : 3030760472 |
This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.
| Author | : Pietro Cerone |
| Publisher | : CRC Press |
| Total Pages | : 394 |
| Release | : 2010-12-01 |
| Genre | : Mathematics |
| ISBN | : 1439848971 |
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
| Author | : Zdravko Cvetkovski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 439 |
| Release | : 2012-01-06 |
| Genre | : Mathematics |
| ISBN | : 3642237924 |
This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.
| Author | : Titu Andreescu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 137 |
| Release | : 2016-12-19 |
| Genre | : Juvenile Nonfiction |
| ISBN | : 1470434644 |
This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not “linear”. The central topic of inequalities is linked to others in mathematics. Often these topics relate to much more than algebraic inequalities. There are also “secret” pathways through the book. Each chapter has a subtext, a theme which prepares the student for learning other mathematical topics, concepts, or habits of mind. For example, the early chapters on the arithmetic mean/geometric mean inequality show how very simple observations can be leveraged to yield useful and interesting results. Later chapters give examples of how one can generalize a mathematical statement. The chapter on the Cauchy-Schwarz inequality provides an introduction to vectors as mathematical objects. And there are many other secret pathways that the authors hope the reader will discover—and follow. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
| Author | : Michael Ruzhansky |
| Publisher | : Springer |
| Total Pages | : 579 |
| Release | : 2019-07-02 |
| Genre | : Mathematics |
| ISBN | : 303002895X |
This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
