Advanced Inequalities
Advanced Inequalities

Author: George A. Anastassiou

Publisher: World Scientific

Published: 2011

Total Pages: 423

ISBN-13: 9814317624

DOWNLOAD EBOOK

This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end. The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and HardyOpial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as ChebyshevGruss, Gruss and Comparison of Means inequalities are studied. The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.

Advances in Matrix Inequalities
Advances in Matrix Inequalities

Author: Mohammad Bagher Ghaemi

Publisher: Springer Nature

Published: 2021-07-11

Total Pages: 287

ISBN-13: 3030760472

DOWNLOAD EBOOK

This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.

Advances in Mathematical Inequalities and Applications
Advances in Mathematical Inequalities and Applications

Author: Praveen Agarwal

Publisher: Springer

Published: 2018-12-31

Total Pages: 351

ISBN-13: 9811330131

DOWNLOAD EBOOK

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.

Advances in Mathematical Inequalities
Advances in Mathematical Inequalities

Author: Shigeru Furuichi

Publisher:

Published: 2020-02-13

Total Pages: 230

ISBN-13: 9783110643435

DOWNLOAD EBOOK

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 which will are applied and further developed in many fields. Applications of the inequalities to entropy theory and quantum physics are also included.

Nonlinear Inclusions and Hemivariational Inequalities
Nonlinear Inclusions and Hemivariational Inequalities

Author: Stanisław Migórski

Publisher: Springer Science & Business Media

Published: 2012-09-18

Total Pages: 293

ISBN-13: 146144232X

DOWNLOAD EBOOK

This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis. Provided results are based on original research on the existence, uniqueness, regularity and behavior of the solution for various classes of nonlinear stationary and evolutionary inclusions. In carrying out the variational analysis of various contact models, one systematically uses results of hemivariational inequalities and, in this way, illustrates the applications of nonlinear analysis in contact mechanics. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation. Contact problems arise in industry, engineering and geophysics. Their variational analysis presented in this book lies the background for their numerical analysis. This volume will interest mathematicians, applied mathematicians, engineers, and scientists as well as advanced graduate students.

Fractional Differentiation Inequalities
Fractional Differentiation Inequalities

Author: George A. Anastassiou

Publisher: Springer Science & Business Media

Published: 2009-05-28

Total Pages: 672

ISBN-13: 0387981284

DOWNLOAD EBOOK

In this book the author presents the Opial, Poincaré, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined. This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians, engineers, and other applied scientists will also find this book useful.

Hardy Inequalities on Homogeneous Groups
Hardy Inequalities on Homogeneous Groups

Author: Michael Ruzhansky

Publisher: Springer

Published: 2019-07-02

Total Pages: 579

ISBN-13: 303002895X

DOWNLOAD EBOOK

This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Global Entangled Inequalities
Global Entangled Inequalities

Author: Elizabeth Jelin

Publisher: Routledge

Published: 2017-11-08

Total Pages: 326

ISBN-13: 1351727885

DOWNLOAD EBOOK

This book presents studies from across Latin America to take up the challenge of exploring the plurality of social inequalities from a global perspective. Accordingly, it identifies the structural forces of social inequalities on a world scale as they shape asymmetries observed in a wide array of phenomena, such as racial and gender inequality, urbanization, migration, commodity production, indigenous mobilization, ecological conflicts, and the "new middle class". A rich contribution to the study of the interconnections between the global social structure and multiple local and national hierarchies, Global Entangled Inequalities brings consistently together a variety of conceptual approaches, ranging from ethnographies to legal genealogies, and will therefore appeal to scholars across the social sciences with interests in social theory, power analysis, intersectionality studies, urban studies, and global social and environmental justice.

Inequalities from Complex Analysis
Inequalities from Complex Analysis

Author: John P. D'Angelo

Publisher:

Published: 2002

Total Pages: 288

ISBN-13: 9780883850008

DOWNLOAD EBOOK

Inequalities from Complex Analysis is a careful, friendly exposition of some rather interesting mathematics. The author begins by defining the complex number field; he gives a novel presentation of some standard mathematical analysis in the early chapters. The development culminates with some results from recent research literature. The book provides complete yet comprehensible proofs as well as some surprising consequences of the results. One unifying theme is a complex variables analogue of Hilbert's seventeenth problem. Numerous examples, exercises and discussions of geometric reasoning aid the reader. The book is accessible to undergraduate mathematicians, as well as physicists and engineers.