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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.
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.
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.
Edited by Nora Lustig, the Commitment to Equity Handbook: Estimating the Impact of Fiscal Policy on Inequality and Poverty (Brookings Institution Press and CEQ Institute-Tulane University, 2nd edition, 2022) is a unique manual on the theory and practical methods to estimate the impact of taxation and public spending on inequality and poverty. In addition, the second edition covers frontier topics such as alternative approaches to measure the redistributive effect of education, health, and infrastructure spending. Policymakers, social planners, and economists are provided with a step-by-step guide to applying fiscal incidence analysis, illustrated by country studies. The 2nd edition of the Handbook has two volumes. Volume 1 is comprised of Part I, Methodology, describes what a CEQ Assessment© is and presents the theoretical underpinnings of fiscal incidence analysis and the indicators used to assess the distributive impact and effectiveness of fiscal policy. Part II, Implementation, presents the methodology on how taxes, subsidies, and social spending should be allocated. It includes a step-by step guide to completing the CEQ Master Workbook©, a multi-sheet Excel file that houses detailed information on the country’s fiscal system and the results used as inputs for policy discussions, academic papers, and policy reports. Part III, “Applications,” presents applications of the CEQ framework to low- and middle-income countries and includes simulations of policy reforms. In this 2nd edition, chapters 1, 6, and 8 have been significantly updated and two new country studies have been added to Part III. Parts IV (updated), V (new), and VI (new) are available online only. Part IV contains the CEQ Assessment’s main tools. Part V includes the databases housed in the CEQ Data Center on Fiscal Redistribution. Part VI contains the CEQ Institute’s microsimulation tools. Volume 2 (new) includes a collection of chapters whose purpose is to expand the knowledge and methodological frontiers to sharpen even further the analysis of fiscal policy’s redistributive impact. Topics include: alternative approaches to value in-kind education and health services; alternative methods to evaluate spending on infrastructure; corporate taxes and taxation on capital incomes; inter-temporal fiscal incidence and the redistributive consequences of social insurance pensions; fiscal redistribution, macroeconomic stability and growth; and, the political economy of fiscal redistribution.
This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.
As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.
"The Handbook on health inequality monitoring: with a special focus on low- and middle-income countries is a resource that enables countries to do just that. It presents a comprehensive yet clear overview of health inequality monitoring in a user-friendly manner. The handbook succeeds in giving those involved in health inequality monitoring an appreciation of the complexities of the process, as well as building the practical knowledge and skills for systematic monitoring of health inequalities in low- and middle-income countries. The use of the handbook will enable countries to better monitor and evaluate their progress and performance with a high degree of accountability and transparency, and allow them to use the results to formulate evidenced-based policies, programmes and practices to tackle inequalities in an effective manner."--Publisher's description.
For anyone wanting to learn, in practical terms, how to measure, describe, monitor, evaluate, and analyze poverty, this Handbook is the place to start. It is designed to be accessible to people with a university-level background in science or the social sciences. It is an invaluable tool for policy analysts, researchers, college students, and government officials working on policy issues related to poverty and inequality.
The literature on inequalities is vast-in recent years the number of papers as well as the number of journals devoted to the subject have increased dramatically. At best, locating a particular inequality within the literature can be a cumbersome task. A Dictionary of Inequalities ends the dilemma of where to turn to find a result, a related inequality, or the references to the information you need. It provides a concise, alphabetical listing of each inequality-by its common name or its subject-with a short statement of the result, some comments, references to related inequalities, and a list of sources for further information. The author uses only the most elementary of mathematical terminology and does not offer proofs, thus making an interest in inequalities the only prerequisite for using the text. The author focuses on intuitive, physical forms of inequalities rather than their most general versions, and retains the beauty and importance of original versions rather than listing their later, abstract forms. He presents each in its simplest form with other renditions, such as for complex numbers and vectors, as extensions or under different headings. He has kept the book to a more manageable size by omitting inequalities in areas-such as elementary geometric and trigonometric inequalities-rarely used outside their fields. The end result is a current, concise, reference that puts the essential results on inequalities within easy reach. A Dictionary of Inequalities carries the beauty and attraction of the best and most successful dictionaries: on looking up a given item, the reader is likely to be intrigued and led by interest to others.