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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-typeinequalities and their extensions on time scales.
List of contents
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
About the author
Ravi P. AgarwalDepartment of Mathematics,Texas A&M University–KingsvilleKingsville, Texas, USA.
Donal O’ReganSchool of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalway, Ireland.
Samir H. SakerDepartment of Mathematics,Mansoura UniversityMansoura, Egypt.
Summary
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-typeinequalities and their extensions on time scales.
Additional text
“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)
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"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)
