Overview
- Provides an analysis of a variety of important integral inequalities
- Using Halanay’s inequalities and the properties of exponential function on time scales, this book establishes new conditions that lead to stability for nonlinear dynamic equations
- Develops a unified approach to handling multiple dynamic systems simultaneously using the recently-developed theory of dynamic systems on time scales
- Includes supplementary material: sn.pub/extras
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About this book
This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics.
In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebyšv's inequality.
Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.
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Keywords
Table of contents (6 chapters)
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Front Matter
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Back Matter
Reviews
“This book represents the state of the art of the current research about dynamic inequalities on time scales … . It serves as a study guide for graduate students in the exciting, rather new, area of dynamic equations on time scales, giving students plenty of ideas how to improve and apply the presented inequalities. … This landmark book should be in the personal library of any researcher interested in inequalities, no matter whether of continuous, discrete, or dynamic type.” (Martin J. Bohner, Mathematical Reviews, April, 2016)
“The present book, which contains six chapters, is devoted to the study of some fundamental dynamic inequalities on time scales … . This book is well written, the results are well presented and proved. … This book is very good and is recommended for graduate students and researchers working in any area of pure and applied mathematics.” (James Adedayo Oguntuase, zbMATH 1318.26002, 2015)
Authors and Affiliations
About the authors
Ravi P Agarwal Department of Mathematics Texas A&M University–Kingsville Kingsville, Texas, USA Donal O’Regan School of Mathematics, Statistics and Applied Mathematics National University of Ireland Galway, Ireland Samir H Saker Department of Mathematics Mansoura University Mansoura, Egypt.
Bibliographic Information
Book Title: Dynamic Inequalities On Time Scales
Authors: Ravi Agarwal, Donal O'Regan, Samir Saker
DOI: https://doi.org/10.1007/978-3-319-11002-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-11001-1Published: 11 November 2014
Softcover ISBN: 978-3-319-36404-9Published: 22 September 2016
eBook ISBN: 978-3-319-11002-8Published: 30 October 2014
Edition Number: 1
Number of Pages: X, 256
Topics: Functional Analysis, Several Complex Variables and Analytic Spaces, Measure and Integration