Описание: Inequalities based on Sobolev Representations deals exclusively with very general tight integral inequalities of Chebyshev-Gr?ss, Ostrowski types and of integral means, all of which depend upon the Sobolev integral representations of functions. Applications illustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions. This book also derives important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. The results are examined in all directions and through both univariate and multivariate cases. This book is suitable for researchers, graduate students, and seminars in subareas of mathematical analysis, inequalities, partial differential equations and information theory.
Описание: Integral inequalities involving functions with bounded derivatives, otherwise known as Ostrowski-type integral inequalities, have enjoyed a surge in popularity. This field has developed significantly over the last few years, and has yielded many new results and powerful applications in numerical integration, probability theory and stochastics, statistics, information theory, and integral operator theory. The main aim of the present work is to present a number of selected results on Ostrowski-type integral inequalities. Results for univariate and multivariate real functions and their natural applications in the error analysis of numerical quadratures for both simple and multiple integrals as well as for the Riemann-Stieltjes integral are given. Topics dealt with include generalisations of the Ostrowski inequality and its applications; integral inequalities for n-times differentiable mappings; three-point quadrature rules; product-branched Peano kernels and numerical integration; Ostrowski-type inequalities for multiple integrals; results for double integrals based on an Ostrowski-type inequality; product inequalities and weighted quadrature; and some inequalities for the Riemann-Stieltjes integral. This book is intended for researchers and graduate students working in the fields of integral inequalities, approximation theory, applied mathematics, probability theory and stochastics, and numerical analysis.
Описание: Complementarity theory, a relatively new domain in applied mathematics, has deep connections with several aspects of fundamental mathematics and also has many applications in optimization, economics and engineering. The study of variational inequalities is another domain of applied mathematics with many applications to the study of certain problems with unilateral conditions. This book is the first to discuss complementarity theory and variational inequalities using LerayвЂ“Schauder type alternatives. The ideas and method presented in this book may be considered as a starting point for new developments.
Название: Weighted inequalities of hardy type ISBN: 9812381953 ISBN-13(EAN): 9789812381958 Издательство: World Scientific Publishing Рейтинг: Цена: 7532 р. Наличие на складе: Поставка под заказ.
Описание: Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This is a survey of the theory of
weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit
(Carleman-Knopp type) inequalities. It also describes some new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone
function together with some applications and open problems.
The book can serve as a reference and a source of inspiration for researchers working in these and related
areas, but could also be used for advanced graduate courses.
Описание: Collecting all the results on the particular types of inequalities, the coverage of this book is unique among textbooks in the literature. The book focuses on the
historical development of the Carlson inequalities and their many generalizations and variations. As well as almost all known results concerning these inequalities and all known proof
techniques, a number of open questions suitable for further research are considered.
Two chapters are devoted to clarifying the close connection between interpolation
theory and this type of inequality. Other applications are also included, in addition to a historical note on Fritz Carlson himself.
Автор: Farit G. Avkhadiev; Karl-Joachim Wirths Название: Schwarz-Pick Type Inequalities ISBN: 3764399996 ISBN-13(EAN): 9783764399993 Издательство: Springer Рейтинг: Цена: 5774 р. Наличие на складе: Поставка под заказ.
Описание: Discusses the extension of the Schwarz-Pick inequality to higher order derivatives of analytic functions with given images. This book presents a systematic account of the main results in this area. It is of interest for researchers and postgraduate students in function theory and hyperbolic geometry.
Автор: Agarwal Название: Hardy Type Inequalities on Time Scales ISBN: 3319442988 ISBN-13(EAN): 9783319442983 Издательство: Springer Рейтинг: Цена: 12704 р. Наличие на складе: Поставка под заказ.
The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and Littlewood type inequalities, Hardy-Knopp type inequalities via convexity, Copson type inequalities, Copson-Beesack type inequalities, Liendeler type inequalities, Levinson type inequalities and Pachpatte type inequalities, Bennett type inequalities, Chan type inequalities, and Hardy type inequalities with two different weight functions. These dynamic inequalities contain the classical continuous and discrete inequalities as special cases when T = R and T = N and can be extended to different types of inequalities on different time scales such as T = hN, h > 0, T = qN for q > 1, etc.In this book the authors followed the history and development of these inequalities. Each section in self-contained and one can see the relationship between the time scale versions of the inequalities and the classical ones. To the best of the authors’ knowledge this is the first book devoted to Hardy-type
Описание: Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy-type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new areas such as higher order and fractional order Hardy-type inequalities and integral inequalities on the cone of monotone functions, together with some applications and open problems.In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions.
Описание: This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Описание: 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.
Описание: Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and l^n p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related to large deviation inequalities in Probability on the one hand, and to isoperimetric inequalities in Geometry on the other. The book contains also an appendix, written by M. Gromov, which is an introduction to isoperimetric inequalities on riemannian manifolds. Only basic knowledge of Functional Analysis and Probability is expected of the reader. The book can be used (and was used by the authors) as a text for a first or second graduate course. The methods used here have been useful also in areas other than Functional Analysis (notably, Combinatorics).
Описание: Provides a systematic account of asymptotic sets and functions from which a useful theory emerges in the areas of optimization and variational inequalities. This book is useful for advanced graduate students, researchers, and practitioners in the fields of optimization theory, nonlinear programming, and applied mathematical sciences.
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