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Iteration of positive approximation operators. (English) Zbl 0199.44702


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[1] Arató, M.; Rényi, A., Probabilistic proof of a theorem on the approximation of continuous functions by means of generalized Bernstein polynomials, Acta Math. Acad. Sci. Hungar., 8, 91-98 (1957) · Zbl 0078.05501
[2] Chernoff, H., A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, Ann. Math. Stat., 23, 493-507 (1952) · Zbl 0048.11804
[3] Hille, E.; Phillips, R., Functional Analysis and Semi-Groups, (Amer. Math. Soc. Colloq. Publ., Vol. 31 (1957)), Providence, R. I.
[4] Karlin, S., Stochastic Processes (1966), Academic Press, Inc: Academic Press, Inc New York
[5] Karlin, S., (Total Positivity, Vol. 1 (1968), Stanford University Press: Stanford University Press Stanford) · Zbl 0219.47030
[6] Karlin, S.; McGregor, J., On a genetics model of Moran, (Proc. Cambridge Philos. Soc., 58 (1962)), 299-311 · Zbl 0218.60073
[7] Kelisky, R. P.; Rivlin, T. J., Iterates of Bernstein polynomials, Pacific J. Math., 21, 511-520 (1967) · Zbl 0177.31302
[8] Konheim, A. G.; Rivlin, T. J., The bounded linear operators that commute with the Bernstein operators, Bull. Amer. Math. Soc., 74, 111-114 (1968) · Zbl 0174.44201
[9] Korovkin, P. P., Linear Operators and Approximation Theory (1960), Hindustani Publ. Co: Hindustani Publ. Co Delhi · Zbl 0094.10201
[10] Kurtz, T. G., Extensions of Trotter’s operator semigroup approximation theorems, J. Funct. Anal., 3, 354-375 (1969) · Zbl 0174.18401
[11] Micchelli, C. A., Saturation Classes and Iterates of Operators, (Ph.D. Thesis (1969), Stanford University) · Zbl 0268.41008
[12] Rényi, A., Summation methods and probability theory, Magyar Tud. Akad. Mat. Kutató Int. Közl., 4, 389-399 (1959) · Zbl 0217.13502
[13] Widder, D. V., The Laplace Transform (1941), Princeton Univ. Press: Princeton Univ. Press Princeton · Zbl 0060.24801
[14] Yosida, K., Functional Analysis (1965), Springer-Verlag: Springer-Verlag Berlin · Zbl 0126.11504
[15] Ziegler, Z., Linear Approximation and Generalized Convexity, J. Approx. Theory, 1, 420-443 (1968) · Zbl 0179.09201
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