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A Korovkin type approximation theorem for set-valued functions


Authors: Klaus Keimel and Walter Roth
Journal: Proc. Amer. Math. Soc. 104 (1988), 819-824
MSC: Primary 41A36
DOI: https://doi.org/10.1090/S0002-9939-1988-0964863-8
MathSciNet review: 964863
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0964863-8
Article copyright: © Copyright 1988 American Mathematical Society