A Korovkin type approximation theorem for set-valued functions
HTML articles powered by AMS MathViewer
- by Klaus Keimel and Walter Roth PDF
- Proc. Amer. Math. Soc. 104 (1988), 819-824 Request permission
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.References
- Heinz Bauer, Theorems of Korovkin type for adapted spaces, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 4, 245–260 (English, with French summary). MR 358178 —, Approximationssätze und abstrakte Ränder, Math. Phys. Sem. Berichte 13 (1976), 141-173.
- H. Berens and G. G. Lorentz, Theorems of Korovkin type for positive linear operators on Banach lattices, Approximation theory (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1973) Academic Press, New York, 1973, pp. 1–30. MR 0340913
- Klaus Donner, Extension of positive operators and Korovkin theorems, Lecture Notes in Mathematics, vol. 904, Springer-Verlag, Berlin-New York, 1982. MR 653635
- H.-O. Flösser, Korovkinsche Approximation stetiger Funktionen, Yearbook: surveys of mathematics 1980 (German), Bibliographisches Inst., Mannheim, 1980, pp. 93–119 (German). MR 620329
- H.-O. Flösser, R. Irmisch, and W. Roth, Infimum-stable convex cones and approximation, Proc. London Math. Soc. (3) 42 (1981), no. 1, 104–120. MR 602125, DOI 10.1112/plms/s3-42.1.104 A. Jung, Stetige Verbände und Approximationssätze, Diplomarbeit, Darmstadt, 1983. H. Minkowski, Theorie der konvexen Körper, insbesondere Begründung ihres Oberflächenbegriffs, Ges. Abhandlungen, Vol. 2, Leipzig, Berlin, 1911, pp. 131-229.
- Richard A. Vitale, Approximation of convex set-valued functions, J. Approx. Theory 26 (1979), no. 4, 301–316. MR 550678, DOI 10.1016/0021-9045(79)90067-4
Additional Information
- © Copyright 1988 American Mathematical Society
- 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