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This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics.
The present volume is part 1 of the author's two-volume work on inequalities.
Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.
List of contents
Preface.- Linear One-Dimensional Continuous Integral Inequalities.- Linear One-Dimensional Discrete (Difference) Inequalities.- Linear One-Dimensional Discontinuous Integral Inequalities.- Applications of Linear One-Dimensional Inequalities.- Linear Multi-Dimensional Continuous Integral Inequalities.- Linear Multi-Dimensional Discrete (Difference) Inequalities.- Linear Multi-Dimensional Discontinuous Integral Inequalities.- Applications of Linear Multi-Dimensional Integral and Difference Inequalities.
Summary
This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics.
The present volume is part 1 of the author’s two-volume work on inequalities.
Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.
Additional text
“The present research book is a useful exposition of mathematical works done by the author, scattered in many papers over the past decades, involving subjects of classical analysis such as integral inequalities and discrete inequalities. … This book provides a useful collection and systematic presentation of known and new results on linear inequalities, as well as many applications to differential, difference and integral equations. This book is useful for researchers working on these topics.” (Choonkil Park, zbMATH 1359.26004, 2017)
