A new class of linear positive operators of Bernstein type
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Baskakov, V.A., An example of a sequence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk., 113(1957), pp. 249-251.
Della Vecchia, B., On monotonicity of some linear positive operators, to appear in "Proceedings of the Third Conference on Numerical Methods and Approximation Theory", Niš, Yugoslavie (1987).
Della Vecchia, B., On the preservation of Lipschitz constants for some linear operators, submitted to "Bollettino della Unione Matematica Italiana" (1987).
Favard, J., Sur les multiplicateurs d'interpolation. (French) J. Math. Pures Appl. (9) 23, (1944). 219-247, MR0015547.
Freedman, David; Passow, Eli Degenerate Bernstein polynomials. J. Approx. Theory 39 (1983), no. 1, 89-92, MR0713364, https://doi.org/10.1016/0021-9045(83)90071-0
Hermann, T. On Baskakov-type operators. Acta Math. Acad. Sci. Hungar. 31 (1978), no. 3-4, 307-316, MR0470572, https://doi.org/10.1007/bf01901980
Horová, Ivana, A note on the sequence formed by the first order derivatives of the Szász-Mirakyan operators. Mathematica (Cluj) 24(47) (1982), no. 1-2, 49-52, MR0692184.
Mastroianni, G., Sui resti di alcune forme lineari di approssimazione, Calcolo, 14 (1978), pp. 343-368.
Mastroianni, Giuseppe A class of positive linear operators. (Italian) Rend. Accad. Sci. Fis. Mat. Napoli (4) 48 (1980/81), 217-235 (1982), MR0697886.
Mastroianni, Giuseppe; Occorsio, Mario Rosario A generalization of the Stancu operator. (Italian) Rend. Accad. Sci. Fis. Mat. Napoli (4) 45 (1978), 495-511 (1979), MR0549902.
Mastroianni, Giuseppe, Occorsio, Mario Rosario, On the derivatives of Stancu polynomials. (Italian) Rend. Accad. Sci. Fis. Mat. Napoli (4) 45 (1978), 273-281 (1979), MR0549893.
Mastroianni, G., Occorsio, M. R., A new operator of Bernstein type. Anal. Numér. Théor. Approx. 16 (1987), no. 1, 55-63, MR0938785.
Mirakyan, G., Approximation des fonctions continues au moyen de polynômes de la forme e-nx∑k=0mCk,nχk. (French) C. R. (Doklady) Acad. Sci. URSS (N.S.) 31, (1941). 201-205, MR0004343.
Moldovan, Elena, Observations sur la suite des polynomes de S. N. Bernstein d'une fonction continue. (French) Mathematica (Cluj) 4 (27) 1962, pp. 289-292, MR0164178.
Popoviciu, Tiberiu Sur le reste dans certaines formules linéaires d'approximation de l'analyse. (French) Mathematica (Cluj) 1 (24) 1959, pp. 95-142, MR0129531.
Stancu, D. D. Approximation of functions by a new class of linear polynomial operators. Rev. Roumaine Math. Pures Appl. 13 1968, pp.1173-1194, MR0238001.
Stancu, D. D., Use of probabilistic methods in the theory of uniform approximation of continuous functions. Rev. Roumaine Math. Pures Appl. 14 1969, pp. 673-69, MR0247338.
Stancu, D. D. Approximation properties of a class of linear positive operators. Studia Univ. Babeş-Bolyai Ser. Math.-Mech. 15 1970 fasc. 2,pp. 33-38, MR0280918.
Stancu, D. D. On the remainder of approximation of functions by means of a parameter-dependent linear polynomial operator. Studia Univ. Babeş-Bolyai Ser. Math.-Mech. 16 (1971), no. 2, pp. 59-66, MR0304941.
Stancu, D. D., Approximation of functions by means of some new classes of positive linear operators. Numerische Methoden der Approximationstheorie, Band 1 (Tagung, Math. Forschungsinst., Oberwolfach, 1971), pp. 187-203. Internat. Schriftenreihe Numer. Math., Band 16, Birkhäuser, Basel, 1972, MR0380207.
Stancu, D. D. Application of divided differences to the study of monotonicity of the derivatives of the sequence of Bernšteĭn polynomials. Calcolo 16 (1979), no. 4, pp. 431-445 (1980), MR0592481.
Stancu, Felicia On the remainder in the approximation formulas by Mirakyan operators of one and two variables. (Romanian) An. Şti. Univ. "Al. I. Cuza" Iaşi Secţ. I a Mat. (N.S.) 14 1968, pp. 415-422, MR0252919.
Stancu, Felicia, On the approximation of functions of one and two variables by means of the operators of Baskakov. (Romanian) Stud. Cerc. Mat. 22 (1970), pp. 531-542, MR0310508.
Szasz, Otto, Generalization of S. Bernstein's polynomials to the infinite interval. J. Research Nat. Bur. Standards 45, (1950), pp. 239-245, MR0045863, https://doi.org/10.6028/jres.045.024
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