Hardy Type Inequalities on Time Scales

Authors: Ravi P. Agarwal, Donal O'Regan, Samir H. Saker



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

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-typeinequalities and their extensions on time scales.

Table of contents

Front Matter
Pages i-x

Hardy and Littlewood Type Inequalities
Pages 1-48

Copson-Type Inequalities
Pages 49-67

Leindler-Type Inequalities
Pages 69-89

Littlewood-Bennett Type Inequalities
Pages 91-120

Weighted Hardy Type Inequalities
Pages 121-151

Levinson-Type Inequalities
Pages 153-219

Hardy-Knopp Type Inequalities
Pages 221-294

Back Matter
Pages 295-305

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