  In this work, we introduce new approximation operators for univariate
set-valued functions with general compact images. We adapt linear approximation
methods for real-valued functions by replacing linear combinations of numbers
with new metric linear combinations of finite sequences of compact sets, thus
obtaining "metric analogues" operators for set-valued functions. The new metric
linear combination extends the binary metric average of Artstein. Approximation
estimates for the metric analogue operators are derived. As examples we study
metric Bernstein operators, metric Shoenberg operators and metric polynomial
interpolants.
