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Hardy Type Inequalities on Time Scales

Ravi P. Agarwal, Donal O'Regan, Samir H. Saker (Autoren)

Buch | Hardcover

X, 305 Seiten

2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-44298-3 (ISBN)

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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.

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.

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

"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)

Erscheinungsdatum	26.11.2016
Zusatzinfo	X, 305 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Copson-Type Inequalities • Functional Analysis • Hardy and Littlewood Type Inequalities • Hardy-Knopp Type Inequalities • Inequalities and Convexity • Inequalities on Time Scales • mathematics and statistics • measure and integration
ISBN-10	3-319-44298-8 / 3319442988
ISBN-13	978-3-319-44298-3 / 9783319442983
Zustand	Neuware