Opial Inequalities with Applications in Differential and Difference Equations
Opial Inequalities with Applications in Differential and Difference Equations

Author: R.P. Agarwal

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 407

ISBN-13: 9401584265

DOWNLOAD EBOOK

In 1960 the Polish mathematician Zdzidlaw Opial (1930--1974) published an inequality involving integrals of a function and its derivative. This volume offers a systematic and up-to-date account of developments in Opial-type inequalities. The book presents a complete survey of results in the field, starting with Opial's landmark paper, traversing through its generalizations, extensions and discretizations. Some of the important applications of these inequalities in the theory of differential and difference equations, such as uniqueness of solutions of boundary value problems, and upper bounds of solutions are also presented. This book is suitable for graduate students and researchers in mathematical analysis and applications.

Difference Equations and Inequalities
Difference Equations and Inequalities

Author: Ravi P. Agarwal

Publisher: CRC Press

Published: 2000-01-27

Total Pages: 1010

ISBN-13: 9781420027020

DOWNLOAD EBOOK

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

Differential and Integral Inequalities: Theory and Applications
Differential and Integral Inequalities: Theory and Applications

Author: V. Lakshmikantham

Publisher: Academic Press

Published: 1969

Total Pages: 405

ISBN-13: 0080955630

DOWNLOAD EBOOK

This volume constitutes the first part of a monograph on theory and applications of differential and integral inequalities. 'The entire work, as a whole, is intended to be a research monograph, a guide to the literature, and a textbook for advanced courses. The unifying theme of this treatment is a systematic development of the theory and applicationsof differential inequalities as well as Volterra integral inequalities. The main tools for applications are the norm and the Lyapunov functions. Familiarity with real and complex analysis, elements of general topology and functional analysis, and differential and integral equations is assumed.

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.

Inequalities Involving Functions and Their Integrals and Derivatives
Inequalities Involving Functions and Their Integrals and Derivatives

Author: Dragoslav S. Mitrinovic

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 602

ISBN-13: 9401135622

DOWNLOAD EBOOK

One service mathematics has rendered the ~l moil ..., Ii j'avait su comment en revenir, je n'y serais point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'(ftre of this series.

Integral and Discrete Inequalities and Their Applications
Integral and Discrete Inequalities and Their Applications

Author: Yuming Qin

Publisher: Birkhäuser

Published: 2016-10-08

Total Pages: 1000

ISBN-13: 3319333011

DOWNLOAD EBOOK

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.

Inequalities for Differential and Integral Equations
Inequalities for Differential and Integral Equations

Author:

Publisher: Elsevier

Published: 1997-11-12

Total Pages: 623

ISBN-13: 0080534643

DOWNLOAD EBOOK

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course. Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books Provides a valuable reference to engineers and graduate students

Mathematical Inequalities
Mathematical Inequalities

Author: B. G. Pachpatte

Publisher: Elsevier

Published: 2005-05-04

Total Pages: 606

ISBN-13: 0080459390

DOWNLOAD EBOOK

The book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics. * It contains a variety of inequalities which find numerous applications in various branches of mathematics.* It contains many inequalities which have only recently appeared in the literature and cannot yet be found in other books.* It will be a valuable reference for someone requiring a result about inequalities for use in some applications in various other branches of mathematics.* Each chapter ends with some miscellaneous inequalities for futher study.* The work will be of interest to researchers working both in pure and applied mathematics, and it could also be used as the text for an advanced graduate course.