Classical And New Inequalities In Analysis
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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.
Classical And New Inequalities In Analysis
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Author : Dragoslav S. Mitrinovic
language : en
Publisher: Springer
Release Date : 2014-03-14
Classical And New Inequalities In Analysis written by Dragoslav S. Mitrinovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-14 with Mathematics categories.
Analytic Inequalities
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Author : Dragoslav S. Mitrinovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analytic Inequalities 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 2012-12-06 with Mathematics categories.
The Theory of Inequalities began its development from the time when C. F. GACSS, A. L. CATCHY and P. L. CEBYSEY, to mention only the most important, laid the theoretical foundation for approximative meth ods. Around the end of the 19th and the beginning of the 20th century, numerous inequalities were proyed, some of which became classic, while most remained as isolated and unconnected results. It is almost generally acknowledged that the classic work "Inequali ties" by G. H. HARDY, J. E. LITTLEWOOD and G. POLYA, which appeared in 1934, transformed the field of inequalities from a collection of isolated formulas into a systematic discipline. The modern Theory of Inequalities, as well as the continuing and growing interest in this field, undoubtedly stem from this work. The second English edition of this book, published in 1952, was unchanged except for three appendices, totalling 10 pages, added at the end of the book. Today inequalities playa significant role in all fields of mathematics, and they present a very active and attractive field of research. J. DIEUDONNE, in his book "Calcullnfinitesimal" (Paris 1968), attri buted special significance to inequalities, adopting the method of exposi tion characterized by "majorer, minorer, approcher". Since 1934 a multitude of papers devoted to inequalities have been published: in some of them new inequalities were discovered, in others classical inequalities ,vere sharpened or extended, various inequalities ,vere linked by finding their common source, while some other papers gave a large number of miscellaneous applications.
Inequalities In Analysis And Probability Third Edition
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Author : Odile Pons
language : en
Publisher: World Scientific
Release Date : 2021-10-18
Inequalities In Analysis And Probability Third Edition written by Odile Pons and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-18 with Mathematics categories.
The book introduces classical inequalities in vector and functional spaces with applications to probability. It develops new analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales, to transformed Brownian motions and diffusions, to Markov and point processes, renewal, branching and shock processes.In this third edition, the inequalities for martingales are presented in two chapters for discrete and time-continuous local martingales with new results for the bound of the norms of a martingale by the norms of the predictable processes of its quadratic variations, for the norms of their supremum and their p-variations. More inequalities are also covered for the tail probabilities of Gaussian processes and for spatial processes.This book is well-suited for undergraduate and graduate students as well as researchers in theoretical and applied mathematics.
Invitation To Classical Analysis
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Author : Peter Duren
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Invitation To Classical Analysis written by Peter Duren 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 2012 with Education categories.
This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities. This book is designed for individual study but can also serve as a text for second-semester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits. Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics.
Inequalities A Journey Into Linear Analysis
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Author : D. J. H. Garling
language : en
Publisher: Cambridge University Press
Release Date : 2007-07-05
Inequalities A Journey Into Linear Analysis written by D. J. H. Garling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Mathematics categories.
This book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.
Mathematical Inequalities
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Author : Pietro Cerone
language : en
Publisher: CRC Press
Release Date : 2010-12-01
Mathematical Inequalities written by Pietro Cerone and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-01 with Mathematics categories.
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
Inequalities And Applications
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Author : Catherine Bandle
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-17
Inequalities And Applications written by Catherine Bandle 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 2008-12-17 with Mathematics categories.
Inequalities continue to play an essential role in mathematics. Perhaps, they form the last field comprehended and used by mathematicians in all areas of the discipline. Since the seminal work Inequalities (1934) by Hardy, Littlewood and Pólya, mathematicians have laboured to extend and sharpen their classical inequalities. New inequalities are discovered every year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. The study of inequalities reflects the many and various aspects of mathematics. On one hand, there is the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand, the subject is the source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are numerous applications in a wide variety of fields, from mathematical physics to biology and economics. This volume contains the contributions of the participants of the Conference on Inequalities and Applications held in Noszvaj (Hungary) in September 2007. It is conceived in the spirit of the preceding volumes of the General Inequalities meetings held in Oberwolfach from 1976 to 1995 in the sense that it not only contains the latest results presented by the participants, but it is also a useful reference book for both lecturers and research workers. The contributions reflect the ramification of general inequalities into many areas of mathematics and also present a synthesis of results in both theory and practice.
Geometric Inequalities
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Author : Hayk Sedrakyan
language : en
Publisher: Springer
Release Date : 2017-05-27
Geometric Inequalities written by Hayk Sedrakyan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-27 with Mathematics categories.
This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities.
Functional Inequalities New Perspectives And New Applications
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Author : Nassif Ghoussoub
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-09
Functional Inequalities New Perspectives And New Applications written by Nassif Ghoussoub 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 2013-04-09 with Mathematics categories.
"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.