An abstract Korovkin type theorem and applications


We obtain some Korovkin type theorems for the space \(C(X)\), where \(X\) is a compact metric space (Theorems 2 and 3).

The results are applied to the case when \(X\) is a compact subspace of a prehilbertian space and we obtain bounds for the difference \(\left \Vert B_{n}(f)-f\right \Vert|), where \(Bn\) is the Bernstein-Lototsky-Schnabl operator


Costica Mustata
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania



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C. Mustăţa, D. Andrica, An abstract Korovkin type theorem and applications, Studia Univ. ”Babeş-Bolyai” XXXIV, fasc. 2 (1989), 44-41.


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Universitatis “Babes-Bolyai” Cluj-Napoca, Romania

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MR # 91j: 41043

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[1] De Vore, Ronald A., The Approximation of Con tinuous Functions by Positive Linear Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1972.
[2] Mamedov, R.G., On the order lf the approximation of differentiable funcitons by linear operators (Russian), Doklady SSSR 128 (1959), 674-676.
[3] Shisha, O., Mond, B., The degree of convergence of sequences of linear pozitive operators,  Proc. Nat. Acad. Sci. USA 60 (1968), 1196-1200.
[4] Nishishiraho, T., The degree of convergence of positive linear operators, Tohoku Math. Journal 29 (1977), 81-89.
[5] Nishishiraho, T., Convergence of positive linear approximation processes, Tohoku Math. Journal 35 (1983), 441-458.

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