Hardy Type Inequalities on Time Scales

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.

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

Autorentext
Ravi P. AgarwalDepartment of Mathematics,Texas A&M UniversityKingsvilleKingsville, Texas, USA.
Donal O'ReganSchool of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalway, Ireland.
Samir H. SakerDepartment of Mathematics,Mansoura UniversityMansoura, Egypt.

Inhalt

1 Hardy and Littlewood Type Inequalities

2 Copson-Type Inequalities

3 Leindler-Type Inequalities

4 Littlewood-Bennett Type Inequalities

5 Weighted Hardy Type Inequalities

6 Levinson-Type Inequalities

7 Hardy-Knopp Type Inequalities

Bibiliography

Index