Abstract
In this paper we introduce new approximation operators for univariate set-valued functions with general compact images in Rn. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new linear combinations of finite sequences of compact sets, thus obtaining metric analogues of these operators for set-valued functions. The new linear combination extends the binary average of Artstein to several sets and admits any real coefficients. Approximation estimates for the analogue operators are derived. As examples we study Bernstein operators, Schoenberg operators, and polynomial interpolants.
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