Inequalities And Applications
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Author |
: Catherine Bandle |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 330 |
Release |
: 2008-12-17 |
ISBN-10 |
: 9783764387730 |
ISBN-13 |
: 3764387734 |
Rating |
: 4/5 (30 Downloads) |
Synopsis Inequalities and Applications by : Catherine Bandle
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.
Author |
: D.D. Bainov |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 254 |
Release |
: 2013-04-18 |
ISBN-10 |
: 9789401580342 |
ISBN-13 |
: 9401580340 |
Rating |
: 4/5 (42 Downloads) |
Synopsis Integral Inequalities and Applications by : D.D. Bainov
This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type. Following a systematic exposition of linear and nonlinear inequalities, attention is paid to analogues including integro-differential inequalities, functional differential inequalities, and discrete and abstract analogues. Applications to the investigation of the properties of solutions of various classes of equations such as uniqueness, stability, dichotomy, asymptotic equivalence and behaviour is also discussed. The book comprises three chapters. Chapter I and II consider classical linear and nonlinear integral inequalities. Chapter III is devoted to various classes of integral inequalities of Gronwall type, and their analogues, which find applications in the theory of integro-differential equations, partial differential equations, differential equations with deviating argument, impube differential equations, etc. Each chapter concludes with a section illustrating the manner of application. The book also contains an extensive bibliography. For researchers whose work involves the theory and application of integral inequalities in mathematics, engineering and physics.
Author |
: Themistocles M. Rassias |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 244 |
Release |
: 2003-09-30 |
ISBN-10 |
: 140201578X |
ISBN-13 |
: 9781402015786 |
Rating |
: 4/5 (8X Downloads) |
Synopsis Functional Equations, Inequalities and Applications by : Themistocles M. Rassias
Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics. This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.
Author |
: Dorin Andrica |
Publisher |
: Springer Nature |
Total Pages |
: 848 |
Release |
: 2019-11-14 |
ISBN-10 |
: 9783030274078 |
ISBN-13 |
: 3030274071 |
Rating |
: 4/5 (78 Downloads) |
Synopsis Differential and Integral Inequalities by : Dorin Andrica
Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.
Author |
: Praveen Agarwal |
Publisher |
: Springer |
Total Pages |
: 351 |
Release |
: 2018-12-31 |
ISBN-10 |
: 9789811330131 |
ISBN-13 |
: 9811330131 |
Rating |
: 4/5 (31 Downloads) |
Synopsis Advances in Mathematical Inequalities and Applications by : Praveen Agarwal
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.
Author |
: Dragoslav S. Mitrinovic |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 739 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9789401710435 |
ISBN-13 |
: 9401710430 |
Rating |
: 4/5 (35 Downloads) |
Synopsis Classical and New Inequalities in Analysis by : Dragoslav S. Mitrinovic
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 |
: Ravi P. Agarwal |
Publisher |
: Springer Nature |
Total Pages |
: 607 |
Release |
: 2021-04-12 |
ISBN-10 |
: 9783030690298 |
ISBN-13 |
: 3030690296 |
Rating |
: 4/5 (98 Downloads) |
Synopsis Lyapunov Inequalities and Applications by : Ravi P. Agarwal
This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov’s inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content.
Author |
: Ravi P. Agarwal |
Publisher |
: CRC Press |
Total Pages |
: 1010 |
Release |
: 2000-01-27 |
ISBN-10 |
: 1420027026 |
ISBN-13 |
: 9781420027020 |
Rating |
: 4/5 (26 Downloads) |
Synopsis Difference Equations and Inequalities by : Ravi P. Agarwal
A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and
Author |
: Mircea Sofonea |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 235 |
Release |
: 2009-04-05 |
ISBN-10 |
: 9780387874609 |
ISBN-13 |
: 0387874607 |
Rating |
: 4/5 (09 Downloads) |
Synopsis Variational Inequalities with Applications by : Mircea Sofonea
This book is motivated by stimulating problems in contact mechanics, emphasizing antiplane frictional contact with linearly elastic and viscoelastic materials. It focuses on the essentials with respect to the qualitative aspects of several classes of variational inequalities (VIs). Clearly presented, easy to follow, and well-referenced, this work treats almost entirely VIs of the second kind, with much of the material being state-of-the-art.
Author |
: Ingram Olkin |
Publisher |
: Academic Press |
Total Pages |
: 590 |
Release |
: 2014-06-28 |
ISBN-10 |
: 9780080959979 |
ISBN-13 |
: 0080959970 |
Rating |
: 4/5 (79 Downloads) |
Synopsis Inequalities by : Ingram Olkin
Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of inequalities." For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations.Anyone wishing to employ majorization as a tool in applications can make use of the theorems; for the most part, their statements are easily understood.