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 prope...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 Part Ⅱ of this series some applications to approximation theory will be shown.展开更多
Fixed points for set_valued mappings from a metric space X (not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.
On the basis of Part (Ⅰ) of this series some applications to the approximation of set_valued functions are obtained: Korovkin type theorems, a method to extend classical approximation operators to the set_valued sett...On the basis of Part (Ⅰ) of this series some applications to the approximation of set_valued functions are obtained: Korovkin type theorems, a method to extend classical approximation operators to the set_valued setting and a Jackson type estimate.展开更多
文摘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 Part Ⅱ of this series some applications to approximation theory will be shown.
文摘Fixed points for set_valued mappings from a metric space X (not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.
文摘On the basis of Part (Ⅰ) of this series some applications to the approximation of set_valued functions are obtained: Korovkin type theorems, a method to extend classical approximation operators to the set_valued setting and a Jackson type estimate.
