Hardy Type Inequalities on Time Scales - Hardcover

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

Hardcover

ISBN 10: 3319442988 ISBN 13: 9783319442983

Publisher: Springer, 2016

Synopsis

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.

About this title

About the Author

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.

From the Back Cover

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-containedand 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.

Edition details

• Publisher: Springer
• Publication date: 2016
• Language: English
• ISBN 10: 3319442988
• ISBN 13: 9783319442983
• Binding: Hardcover
• Edition number: 1
• Number of pages: 315