Hardy Type Inequalities on Time Scales - Agarwal, Ravi;Saker, Samir
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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…mehr

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Produktbeschreibung
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.
Autorenporträt
Sumati Kumari Panda, Ph.D., is a Professor of Mathematics at the GMR Institute of Technology, India. Her research areas include fractional calculus, fixed point theory, neural networks, and their applications. She has published more than 100 research papers in reputed international journals and presented her work at several national and international conferences. She is currently serving as an Academic Editor for Scientific Reports (Springer, Scopus & SCIE-indexed). Dr. Panda received her Ph.D. in Mathematics from K.L. University in 2015. Velusamy Vijayakumar, Ph.D., is an Assistant Professor at the Vellore Institute of Technology (VIT), Vellore, India. His research interests include fractional calculus, dynamical systems, mathematical control theory, and neural networks. Dr. Vijayakumar has authored over 220 research articles in reputed scientific journals. Dr. Vijayakumar received his B.Sc, M.Sc, M.Phil, and Ph.D. degrees in Mathematics from Bharathiar University, Coimbatore, Tamil Nadu, India, in 2002, 2004, 2006, and 2016 respectively. Ravi P. Agarwal, Ph.D., is an Emeritus Research Professor in the Department of Mathematics and Systems Engineering at the Florida Institute of Technology (USA). He has authored or co-authored more than 50 books and more than 2,000 research articles. He has received numerus honors and awards from several universities of the world. His research interests include nonlinear analysis, differential and difference equations, fixed point theory, and general inequalities. Dr. Agarwal received his Ph.D. at the Indian Institute of Technology, Madras, India, in 1973.
Rezensionen
"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)