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© 2016

Hardy Type Inequalities on Time Scales

Book

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

  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

About the authors

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.

Bibliographic information

Industry Sectors
Finance, Business & Banking

Reviews

“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)