Abstract
Ever since Korovkin published his celebrated theorem on the convergence of sequences of positive linear operators in 1953, it has been the study of numerous extensions and generalizations.
Supported by the National Science Foundation and the Alexander von Humboldt-Stiftung.
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References
Ando, T., Contractive projections in L spaces. Pacific J.Math. 17 (1966), 391–405.
Berens, H. — Lorentz, G.G., Sequences of contractions on L1 -spaces. J.Functional Analysis 15 (1974), 155–165.
Berens, H. — Lorentz, G.G., Theorems of Korovkin type for positive linear operators on Banach lattices. In: Approximation Theory, edited by G.G. Lorentz, Academic Press, New York, 1973, pp.1–30.
Bernau, S.J., Theorems of Korovkin type for Lp — spaces. Pacific J. Math. To appear.
Birkhoff, G., Lattice Theory. 3rd ed., Amer.Math.Soc.Coll.Publ. 25, New York 1973.
Douglas, R.G., Contractive projections on an L1 space. Pacific J.Math. 15 (1965), 443–462.
Dzjadyk, V.K., Approximation of functions by positive linear operators and singular integrals (Russian). Math.Sbornik (N.S.) 70(112) (1966), 508–517.
Halperin, I., Uniform convexity in function spaces. Duke Math.J. 21 (1954), 195–204.
Korovkin, P.P., Linear Operators and Approximation Theory, translated from the Russian, Gordon and Breach, New York, 1960.
Lorentz, G.G., Korovkin Sets (Sets of Convergence). Lecture Notes, Regional Conference at the University of California, Riverside, June 15–19, 1972.
Šaškin, Yu.A., On convergence of contraction operators (Russian). Math.Cluj. 11 (34) (1969), 355–360.
Vulikh, B.Z., Introduction to the Theory of Partially Ordered Spaces, translated of the Russian. Wolters-Noordhoff, Groningen 1967.
Wulbert, D.E., Convergence of operators and Korovkin’s theorem. J.Approximation Theory 1 (1968), 381–390.
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Berens, H., Lorentz, G.G. (1974). Korovkin Theorems for Sequences of Contractions on LP-Spaces. In: Butzer, P.L., Szőkefalvi-Nagy, B. (eds) Linear Operators and Approximation II / Lineare Operatoren und Approximation II. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 25. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5991-2_29
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DOI: https://doi.org/10.1007/978-3-0348-5991-2_29
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