Hardy Type Inequalities on Time Scales

  • Ravi P. Agarwal
  • Donal O'Regan
  • Samir H. Saker

Table of contents

  1. Front Matter
    Pages i-x
  2. Ravi P. Agarwal, Donal O’Regan, Samir H. Saker
    Pages 1-48
  3. Ravi P. Agarwal, Donal O’Regan, Samir H. Saker
    Pages 49-67
  4. Ravi P. Agarwal, Donal O’Regan, Samir H. Saker
    Pages 69-89
  5. Ravi P. Agarwal, Donal O’Regan, Samir H. Saker
    Pages 91-120
  6. Ravi P. Agarwal, Donal O’Regan, Samir H. Saker
    Pages 121-151
  7. Ravi P. Agarwal, Donal O’Regan, Samir H. Saker
    Pages 153-219
  8. Ravi P. Agarwal, Donal O’Regan, Samir H. Saker
    Pages 221-294
  9. Back Matter
    Pages 295-305

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Ravi P. Agarwal
    • 1
  • Donal O'Regan
    • 2
  • Samir H. Saker
    • 3
  1. 1.Department of MathematicsTexas A&M University–KingsvilleKingsvilleUSA
  2. 2.School of Mathematics Statistics and Applied MathematicsNational University of IrelandGalwayIreland
  3. 3.Department of MathematicsMansoura UniversityMansouraEgypt

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-44299-0
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-44298-3
  • Online ISBN 978-3-319-44299-0
  • About this book