A Study of Some Classical Inequalities and Their Generalizations
| Author | : |
| Publisher | : |
| Total Pages | : |
| Release | : 2000 |
| Genre | : |
| ISBN | : |
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Generalizations of Some Classical Inequalities and Their Applications
| Author | : Lars Erik Persson |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 1990 |
| Genre | : |
| ISBN | : |
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Survey on Classical Inequalities
| Author | : Themistocles RASSIAS |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 241 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401143390 |
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Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp -norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email address:[email protected] DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: [email protected] Abstract. For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential equations as well as Hamiltonian systems. 1. Introduction Lyapunov's inequality has proved useful in the study of spectral properties of ordinary differential equations. Typical applications include bounds for eigenvalues, stability criteria for periodic differential equations, and estimates for intervals of disconjugacy.
Finite Sections of Some Classical Inequalities
| Author | : Herbert S. Wilf |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 90 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 364286712X |
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Hardy, Littlewood and P6lya's famous monograph on inequalities [17J has served as an introduction to hard analysis for many mathema ticians. Some of its most interesting results center around Hilbert's inequality and generalizations. This family of inequalities determines the best bound of a family of operators on /p. When such inequalities are restricted only to finitely many variables, we can then ask for the rate at which the bounds of the restrictions approach the uniform bound. In the context of Toeplitz forms, such research was initiated over fifty years ago by Szego [37J, and the chain of ideas continues to grow strongly today, with fundamental contributions having been made by Kac, Widom, de Bruijn, and many others. In this monograph I attempt to draw together these lines of research from the point of view of sharpenings of the classical inequalities of [17]. This viewpoint leads to the exclusion of some material which might belong to a broader-based discussion, such as the elegant work of Baxter, Hirschman and others on the strong Szego limit theorem, and the inclusion of other work, such as that of de Bruijn and his students, which is basically nonlinear, and is therefore in some sense disjoint from the earlier investigations. I am grateful to Professor Halmos for inviting me to prepare this volume, and to Professors John and Olga Todd for several helpful comments. Philadelphia, Pa. H.S.W.
Classical and New Inequalities in Analysis
| Author | : Dragoslav S. Mitrinovic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 739 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 9401710430 |
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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.
Factorizing the Classical Inequalities
| Author | : Grahame Bennett |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 145 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821804367 |
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This memoir describes a new way of looking at the classical inequalities. The most famous such results, (those of Hilbert, Hardy, and Copson) may be interpreted as inclusion relationships, l[superscript italic]p [subset equality symbol] [italic capital]Y, between certain (Banach) sequence spaces, the norm of the injection being the best constant of the particular inequality. The inequalities of Hilbert, Hardy, and Copson all share the same space [italic capital]Y. That space -- alias [italic]ces([italic]p) -- is central to many celebrated inequalities, and thus is studied here in considerable detail.
Inequalities
| Author | : Shigeru Furuichi |
| Publisher | : MDPI |
| Total Pages | : 204 |
| Release | : 2020-01-15 |
| Genre | : Mathematics |
| ISBN | : 3039280627 |
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Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.
Advances in Mathematical Inequalities
| Author | : Shigeru Furuichi |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 267 |
| Release | : 2020-01-20 |
| Genre | : Mathematics |
| ISBN | : 3110643472 |
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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. They will be applied and further developed in many fields. Applications of the inequalities to entropy theory and quantum physics are also included.
A Generalization of Probabilistic Cauchy-Schwarz Inequality
| Author | : Roland Forson |
| Publisher | : |
| Total Pages | : 6 |
| Release | : 2017 |
| Genre | : |
| ISBN | : |
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This paper gives a generalization of the probabilistic form of Cauchy-Schwarz inequality and makes a related research on a special case. The classical conclusions of some discrete Cauchy-Schwarz inequalities are generalized to the probability space.
General Inequalities 7
| Author | : Catherine Bandle |
| Publisher | : Birkhäuser |
| Total Pages | : 398 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034889429 |
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Inequalities continue to play an essential role in mathematics. The subject is per haps the last field that is comprehended and used by mathematicians working in all the areas of the discipline of mathematics. Since the seminal work Inequalities (1934) of Hardy, Littlewood and P6lya mathematicians have laboured to extend and sharpen the earlier classical inequalities. New inequalities are discovered ev ery year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. So extensive are these developments that a new mathematical periodical devoted exclusively to inequalities will soon appear; this is the Journal of Inequalities and Applications, to be edited by R. P. Agar wal. Nowadays it is difficult to follow all these developments and because of lack of communication between different groups of specialists many results are often rediscovered several times. Surveys of the present state of the art are therefore in dispensable not only to mathematicians but to the scientific community at large. The study of inequalities reflects the many and various aspects of mathemat ics. There is on the one hand the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand the subject is a source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are many applications in a wide variety of fields from mathematical physics to biology and economics.
