Hardy Type Inequalities on Time Scales

1. Front Matter

   Pages i-x

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2. Hardy and Littlewood Type Inequalities

   • Ravi P. Agarwal, Donal O’Regan, Samir H. Saker

   Pages 1-48

3. Copson-Type Inequalities

   • Ravi P. Agarwal, Donal O’Regan, Samir H. Saker

   Pages 49-67

4. Leindler-Type Inequalities

   • Ravi P. Agarwal, Donal O’Regan, Samir H. Saker

   Pages 69-89

5. Littlewood-Bennett Type Inequalities

   • Ravi P. Agarwal, Donal O’Regan, Samir H. Saker

   Pages 91-120

6. Weighted Hardy Type Inequalities

   • Ravi P. Agarwal, Donal O’Regan, Samir H. Saker

   Pages 121-151

7. Levinson-Type Inequalities

   • Ravi P. Agarwal, Donal O’Regan, Samir H. Saker

   Pages 153-219

8. Hardy-Knopp Type Inequalities

   • Ravi P. Agarwal, Donal O’Regan, Samir H. Saker

   Pages 221-294

9. Back Matter

   Pages 295-305

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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.

• Hardy and Littlewood Type Inequalities
• Copson-Type Inequalities
• Inequalities on Time Scales
• Inequalities and Convexity
• Hardy-Knopp Type Inequalities

“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)

• Department of Mathematics, Texas A&M University–Kingsville, Kingsville, USA

  Ravi P. Agarwal

• School of Mathematics Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

  Donal O'Regan

• Department of Mathematics, Mansoura University, Mansoura, Egypt

  Samir H. Saker

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.

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