Hardy Type Inequalities on Time Scales

ISBN-13: 9783319830346 / Angielski / Miękka / 2018 / 305 str.

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

Recenzje

"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)

Spis treści

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 

O autorze

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.

Blurb

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.