Approximation of continuous convex-cone-valued functions by monotone operators

• Autorzy: João B. Prolla
• Języki publikacji: EN

Abstrakty

EN

In this paper we study the approximation of continuous functions F, defined on a compact Hausdorff space S, whose values F(t), for each t in S, are convex subsets of a normed space E. Both quantitative estimates (in the Hausdorff semimetric) and Bohman-Korovkin type approximation theorems for sequences of monotone operators are obtained.

Kategorie tematyczne

• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 41A35: Approximation by operators (in particular, by integral operators)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 102
• Numer: 2
• Strony: 175-192

Daty

wydano

1992

otrzymano

1991-10-04

Twórcy

autor

João B. Prolla

• Departamento de Matemática, IMECC - UNICAMP, Caixa Postal 6065, 13081 Campinas, Sp, Brazil
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Bibliografia

• [1] R. DeVore, The Approximation of Continuous Functions by Positive Linear Operators, Lecture Notes in Math. 293, Springer, Berlin 1972.
• [2] Z. Ditzian, Inverse theorems for multidimensional Bernstein operators, Pacific J. Math. 121 (1986), 293-319.
• [3] M. W. Grossman, Note on a generalized Bohman-Korovkin theorem, J. Math. Anal. Appl. 45 (1974), 43-46.
• [4] K. Keimel and W. Roth, A Korovkin type approximation theorem for set-valued functions, Proc. Amer. Math. Soc. 104 (1988), 819-824.
• [5] O. Shisha and B. Mond, The degree of convergence of linear positive operators, Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 1196-1200.
• [6] R. A. Vitale, Approximation of convex set-valued functions, J. Approx. Theory 26 (1979), 301-316.