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Saturation of positive operators. (English) Zbl 0233.41007

##### MSC:
 41A40 Saturation (approximations and expansions) 41A36 Approximation by positive operators 41A35 Approximation by operators (in particular, by integral operators)
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##### References:
 [1] Amel’kovic, V. G.: A theorem converse to a theorem of voronovskaja type. Teor. funkčii\check{}, funkčional. Anal. i priložen. 2, 67-74 (1966) [2] Bajanski, B.; Bojanić, R.: A note on approximation by Bernstein polynomials. Bull. amer. Math. soc. 70, 675-677 (1964) [3] Butzer, P. L.; Berens, H.: Semigroups of operators and approximation. (1967) · Zbl 0164.43702 [4] Cheney, E. W.; Sharma, A.: Bernstein power series. Canad. J. Math. 16, 241-253 (1964) · Zbl 0128.29001 [5] Courant, R.; Hilbert, D.: 3rd edition methods of mathematical physics. Methods of mathematical physics (1962) · Zbl 0099.29504 [6] De Leeuw, K.: On the degree of approximation by Bernstein polynomials. J. d’anal. 7, 89-104 (1959) · Zbl 0094.10601 [7] Deluca, L. J.: Algebraic approximation and saturation classes. Ph.d. dissertation (June 1966) [8] Ikeno, K.; Suzuki, Y.: Some remarks on saturation problem in the local approximation. Tôhoku math. J. 20, 214-233 (1968) · Zbl 0215.46402 [9] Karlin, S. J.: 3rd edition total positivity. Total positivity 1 (1968) [10] Karlin, S. J.; Studden, W. J.: Tchebycheff systems. (1966) · Zbl 0153.38902 [11] Karlin, S.; Ziegler, Z.: Iteration of positive approximation operators. J. approximation theory 3, 310-339 (1970) · Zbl 0199.44702 [12] Lorentz, G. G.: Bernstein polynomials. (1953) [13] Lorentz, G. G.: Inequalities and saturation classes of Bernstein polynomials. Proc. conference oberwolfach, 1963, 200-207 (1964) [14] C. A. Micchelli, The saturation classes and iterates of Bernstein operators, to appear in J. Approximation Theory. · Zbl 0258.41012 [15] Mühlbach, G.: Operatoren vom bernsteinschen typ. J. approximation theory 3, 274-292 (1970) · Zbl 0197.04701 [16] Mühlbach, G.: Über das approximationsverhalten gewisser positiver linearer operatoren. Dissertation, 93 (1969) [17] G. Mühlbach, A recurrence formula for generalized divided differences and some applications, to appear in J. Approximation Theory. [18] R. Schnabl, Zum globalen Saturationsproblem der Folge der Bernsteinoperatoren, Acta Math. Szeged, to appear. · Zbl 0204.45404 [19] Stancu, D. D.: Some polynomials of two variables of type Bernstein and some of their applications. Dokl. akad. Nauk SSSR 134, 48-52 (1960) · Zbl 0142.31102 [20] Stancu, D. D.: Evaluation of the remainder term in approximation formulas by Bernstein polynomials. Math. comp. 17, 270-278 (1963) · Zbl 0114.27102 [21] Suzuki, Y.: Saturation of local approximation by linear positive operators of Bernstein type. Tôhoku math. J. 19, 429-453 (1967) · Zbl 0215.46401 [22] Suzuki, Y.; Watanabe, S.: Some remarks on saturation problem in the local approximation. Tôhoku math. J. 21, 65-83 (1969) · Zbl 0215.46403 [23] Watanabe, S.; Suzuki, Y.: Approximation of functions by generalized Meyer-könig and zeller operators. Bull. yamagata univ. (Nat. Science) 7, 123-128 (1969)