This book is aimed at the approximation of set-valued functions
with compact sets in an Euclidean space as values. The interest in
set-valued functions is rather new. Such functions arise in various
modern areas such as control theory, dynamical systems and
optimization. The authors' motivation also comes from the newer
field of geometric modeling, in particular from the problem of
reconstruction of 3D objects from 2D cross-sections. This is
reflected in the focus of this book, which is the approximation of
set-valued functions with general (not necessarily convex) sets as
values, while previous results on this topic are mainly confined to
the convex case. The approach taken in this book is to adapt
classical approximation operators and to provide error estimates in
terms of the regularity properties of the approximated set-valued
functions. Specialized results are given for functions with 1D sets
as values.
General
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