Abstract
A way to extend operators in spaces of continuous functions to spaces of continuous set-valued functions is proposed. This extension is developed through the Steiner selections of the set-valued functions. Their properties and characteristics of the convergence of sequences of operators of this class are studied. In PartII of this series some applications to approximation theory will be shown.
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Communicated by ZHANG Shi-sheng
Foundation items: the Spanish FPI Grant (98-71701353); the DGES Grant (PB98-1534); the DGESIC Grant (PB97-1286)
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Terán, P., López-Dían, M. Set-valued extension of operators via Steiner selections (I)—Theoretical results. Appl Math Mech 23, 568–579 (2002). https://doi.org/10.1007/BF02437775
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DOI: https://doi.org/10.1007/BF02437775