A Study of Some Classical Inequalities and Their Generalizations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download A Study of Some Classical Inequalities and Their Generalizations PDF full book. Access full book title A Study of Some Classical Inequalities and Their Generalizations by . Download full books in PDF and EPUB format.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Lars Erik Persson
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
Get Book Here
Book Description
Author: Themistocles RASSIAS
Publisher: Springer Science & Business Media
ISBN: 9401143390
Category : Mathematics
Languages : en
Pages : 241
Get Book Here
Book Description
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.
Author: Herbert S. Wilf
Publisher: Springer Science & Business Media
ISBN: 364286712X
Category : Mathematics
Languages : en
Pages : 90
Get Book Here
Book Description
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.
Author: Dragoslav S. Mitrinovic
Publisher: Springer Science & Business Media
ISBN: 9401710430
Category : Mathematics
Languages : en
Pages : 739
Get Book Here
Book Description
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.
Author: Grahame Bennett
Publisher: American Mathematical Soc.
ISBN: 0821804367
Category : Mathematics
Languages : en
Pages : 145
Get Book Here
Book Description
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.
Author: Shigeru Furuichi
Publisher: MDPI
ISBN: 3039280627
Category : Mathematics
Languages : en
Pages : 204
Get Book Here
Book Description
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.
Author: Shigeru Furuichi
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110643472
Category : Mathematics
Languages : en
Pages : 267
Get Book Here
Book Description
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.
Author: Roland Forson
Publisher:
ISBN:
Category :
Languages : en
Pages : 6
Get Book Here
Book Description
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.
Author: Hans P. Heinig
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
Get Book Here
Book Description
