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.
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