This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics.
In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Cebysv's inequality.
Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.
Preliminaries.- Basic Inequalities.- Opial Inequalities.- Lyapunov Inequalities.- Halanay Inequalities.- Wirtinger Inequalities. 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.
"This book represents the state of the art of the current research about dynamic inequalities on time scales ... . It serves as a study guide for graduate students in the exciting, rather new, area of dynamic equations on time scales, giving students plenty of ideas how to improve and apply the presented inequalities. ... This landmark book should be in the personal library of any researcher interested in inequalities, no matter whether of continuous, discrete, or dynamic type." (Martin J. Bohner, Mathematical Reviews, April, 2016)
"The present book, which contains six chapters, is devoted to the study of some fundamental dynamic inequalities on time scales ... . This book is well written, the results are well presented and proved. ... This book is very good and is recommended for graduate students and researchers working in any area of pure and applied mathematics." (James Adedayo Oguntuase, zbMATH 1318.26002, 2015)
