Means And Their Inequalities
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Handbook Of Means And Their Inequalities
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Author : P.S. Bullen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Handbook Of Means And Their Inequalities written by P.S. Bullen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
There seems to be two types of books on inequalities. On the one hand there are treatises that attempt to cover all or most aspects of the subject, and where an attempt is made to give all results in their best possible form, together with either a full proof or a sketch of the proof together with references to where a full proof can be found. Such books, aimed at the professional pure and applied mathematician, are rare. The first such, that brought some order to this untidy field, is the classical "Inequalities" of Hardy, Littlewood & P6lya, published in 1934. Important as this outstanding work was and still is, it made no attempt at completeness; rather it consisted of the total knowledge of three front rank mathematicians in a field in which each had made fundamental contributions. Extensive as this combined knowledge was there were inevitably certain lacunre; some important results, such as Steffensen's inequality, were not mentioned at all; the works of certain schools of mathematicians were omitted, and many important ideas were not developed, appearing as exercises at the ends of chapters. The later book "Inequalities" by Beckenbach & Bellman, published in 1961, repairs many of these omissions. However this last book is far from a complete coverage of the field, either in depth or scope.
Means And Their Inequalities
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Author : P.S. Bullen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Means And Their Inequalities written by P.S. Bullen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Approach your problems from the right end It isn't !hat they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal 0/ Fa/her 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuJik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fie1ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "complete1y integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing c1assification schemes. They draw upon wide1y different sections of mathematics.
Handbook Of Means And Their Inequalities
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Author : P.S. Bullen
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-08-31
Handbook Of Means And Their Inequalities written by P.S. Bullen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-31 with Mathematics categories.
This is a revision of an earlier Means and Their Inequalities by the present author and Professors Mitrinovic and Vasic. Not only does this book bring the earlier version up to date but enlarges the scope considerably to give a full and in-depth treatment of all aspects of the field. While the mention of means occurs in many books this is the only full treatment of the subject. Outstanding features of the book are the variety of proofs given for many of the basic results, over seventy for the inequality between the arithmetic and geometric means for instance, an exhaustive bibliography and a list of mathematicians who have contributed to this field from the time of Euclid to the present day. Audience: This book is written in a language that not only the expert on the subject will understand and appreciate, but graduate students worldwide as well. Any person with an interest in means and their inequalities should find this book within their comprehension although to fully appreciate all the topics covered a knowledge of calculus and of elementary real analysis is required.
Inequalities
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Author : Zdravko Cvetkovski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-06
Inequalities written by Zdravko Cvetkovski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-06 with Mathematics categories.
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.
Inequalities
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Author : Radmila Bulajich Manfrino
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-01
Inequalities written by Radmila Bulajich Manfrino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
Positive Definiteness Of Functions With Applications To Operator Norm Inequalities
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Author : Hideki Kosaki
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-06-10
Positive Definiteness Of Functions With Applications To Operator Norm Inequalities written by Hideki Kosaki and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-10 with Mathematics categories.
Positive definiteness is determined for a wide class of functions relevant in the study of operator means and their norm comparisons. Then, this information is used to obtain an abundance of new sharp (unitarily) norm inequalities comparing various operator means and sometimes other related operators.
Classical And New Inequalities In Analysis
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Author : Dragoslav S. Mitrinovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Classical And New Inequalities In Analysis written by Dragoslav S. Mitrinovic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This volume presents a comprehensive compendium of classical and new inequalities as well as some recent extensions to well-known ones. Variations of inequalities ascribed to Abel, Jensen, Cauchy, Chebyshev, Hölder, Minkowski, Stefferson, Gram, Fejér, Jackson, Hardy, Littlewood, Po'lya, Schwarz, Hadamard and a host of others can be found in this volume. The more than 1200 cited references include many from the last ten years which appear in a book for the first time. The 30 chapters are all devoted to inequalities associated with a given classical inequality, or give methods for the derivation of new inequalities. Anyone interested in equalities, from student to professional, will find their favorite inequality and much more.
The Inner Level
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Author : Richard Wilkinson
language : en
Publisher: Penguin UK
Release Date : 2018-06-07
The Inner Level written by Richard Wilkinson and has been published by Penguin UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Social Science categories.
Why is the incidence of mental illness in the UK twice that in Germany? Why are Americans three times more likely than the Dutch to develop gambling problems? Why is child well-being so much worse in New Zealand than Japan? As this groundbreaking study demonstrates, the answer to all these hinges on inequality. In The Spirit Level Richard Wilkinson and Kate Pickett put inequality at the centre of public debate by showing conclusively that less-equal societies fare worse than more equal ones across everything from education to life expectancy. The Inner Level now explains how inequality affects us individually, how it alters how we think, feel and behave. It sets out the overwhelming evidence that material inequalities have powerful psychological effects: when the gap between rich and poor increases, so does the tendency to defi ne and value ourselves and others in terms of superiority and inferiority. A deep well of data and analysis is drawn upon to empirically show, for example, that low social status is associated with elevated levels of stress, and how rates of anxiety and depression are intimately related to the inequality which makes that status paramount. Wilkinson and Pickett describe how these responses to hierarchies evolved, and why the impacts of inequality on us are so severe. In doing so, they challenge the conception that humans are innately competitive and self-interested. They undermine, too, the idea that inequality is the product of 'natural' differences in individual ability. This book sheds new light on many of the most urgent problems facing societies today, but it is not just an index of our ills. It demonstrates that societies based on fundamental equalities, sharing and reciprocity generate much higher levels of well-being, and lays out the path towards them.
Advanced Inequalities
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Author : George A. Anastassiou
language : en
Publisher: World Scientific
Release Date : 2011
Advanced Inequalities written by George A. Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.