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Direct result on exponential-type operators. (English) Zbl 1181.41040

The author studies here the properties of Voronovskaia type for the exponential type operators (Bernstein, Szasz-Mirakian and Baskakov) in simultaneous approximation. He also gives some recurrence relations of some mixed summation-integrable type operators.
Reviewer: Emil Popa (Sibiu)

MSC:

41A36 Approximation by positive operators
41A28 Simultaneous approximation
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References:

[1] Baskakov, V. A., An example of a sequence of linear positive operators in the space of continuous functions, DAN, 113, 249-251 (1957), in Russian · Zbl 0080.05201
[2] Bernstein, S. N., Démonstration du théoréme de Weierstrass fondée sur le calcul de probabilités, Commun. Sco. Math. Charkov, 13, 2, 1-2 (1912)
[3] Deo, N.; Noor, M. A.; Siddiqui, M. A., On approximation by a class of new Bernstein type operators, Appl. Math. Comput., 201, 604-612 (2008) · Zbl 1173.41011
[4] Derriennic, M. M., Surl’approximation des fonctions integrables sur [0,1] par des polynomes de Bernstein modifies, J. Approx. Theory, 31, 325-343 (1981) · Zbl 0475.41025
[5] J.L. Durrmeyer, Une formule d’inversion de la transformée de Laplace-applications à la théorie des moments, Thése de 3e cycle, Faculté des Sciences de l’ Université de Paris, 1967.; J.L. Durrmeyer, Une formule d’inversion de la transformée de Laplace-applications à la théorie des moments, Thése de 3e cycle, Faculté des Sciences de l’ Université de Paris, 1967.
[6] Heilmann, M., Direct and converse results for operators of Baskakov-Durrmeyer type, Approx. Theory Appl., 5, 1, 105-127 (1989) · Zbl 0669.41014
[7] M. Heilmann, M.W. Müller, Direct and converse results on simultaneous approximation by the method of Bernstein-Durrmeyer operators, Dissertation, Universität Dortmund, 1987.; M. Heilmann, M.W. Müller, Direct and converse results on simultaneous approximation by the method of Bernstein-Durrmeyer operators, Dissertation, Universität Dortmund, 1987.
[8] Gupta, V.; Noor, M. A., Convergence of derivatives for certain mixed Szász Beta operators, J. Math. Anal. Appl., 321, 1, 1-9 (2006) · Zbl 1112.41020
[9] Kasana, H. S.; Prasad, G.; Agrawal, P. N.; Sahai, A., Modified Szâsz Operators, Conference on Mathematica Analysis and its Applications, Kuwait (1985), Pergamon Press: Pergamon Press Oxford, pp. 29-41 · Zbl 0717.41041
[10] Mazhar, S. M.; Totik, V., Approximation by modified Szász operators, Acta Sci. Math., 49, 257-269 (1985) · Zbl 0611.41013
[11] Sahai, A.; Prasad, G., On simultaneous approximation by modified Lupas operators, J. Approx. Theory, 45, 122-128 (1985) · Zbl 0596.41035
[12] Szâsz, O., Generalization of S. Bernstein’s polynomials to the infinite interval, NBSJ, J. Res. Nat. Bureau Stand., 45, 239-245 (1950) · Zbl 1467.41005
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