Springer Hardy Type Inequalities on Time Scales

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. Review “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) From the Back Cover 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. About the Author 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.