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 = h N, h > 0, T = q N 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.
विषयसूची
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
लेखक के बारे में
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.
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