Overview
- Provides an analysis of a variety of important Hardy Type inequalities
- Using Hardy Type inequalities and the properties of convexity on time scales, this book establishes new conditions that lead to stability for nonlinear dynamic equations
- Uses a differential equation model for covering a brought subset of inequalities on timescales
- Includes supplementary material: sn.pub/extras
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About this book
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
inequalities and their extensions on time scales.
inequalities and their extensions on time scales.
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Keywords
Table of contents (7 chapters)
Reviews
“This excellent book gives an extensive indept study of the time-scale versions of the classical Hardy-type inequalities, its extensions, refinements and generalizations. … book is self-contained and the relationship between the time scale versions of the inequalities and the classical ones is well discussed. This book is very rich with respect to the historical developments of Hardy-type inequalities on time scales and will be a good reference material for researchers and graduate students working in this investigative area of research.” (James Adedayo Oguntuase, zbMATH 1359.26002, 2017)
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.
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: Hardy Type Inequalities on Time Scales
Authors: Ravi P. Agarwal, Donal O'Regan, Samir H. Saker
DOI: https://doi.org/10.1007/978-3-319-44299-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-44298-3Published: 15 November 2016
Softcover ISBN: 978-3-319-83034-6Published: 28 June 2018
eBook ISBN: 978-3-319-44299-0Published: 20 October 2016
Edition Number: 1
Number of Pages: X, 305