A Korovkin type approximation theorem for set-valued functions

Abstract:

This paper is a contribution to the problem of approximating continuous functions $F$ defined on a compact Hausdorff space $X$, where the value $F(x)$ is a compact convex set in ${{\mathbf {R}}^n}$ for every $x$ in $X$. More specifically we show how to transfer Korovkin type approximation theorems for real-valued continuous functions to this set-valued situation.