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Keywords:
Picard operator; exponential weighted space; degree of approximation; Voronovskaya type theorem
Picard operator; exponential weighted space; degree of approximation; Voronovskaya type theorem
Summary:
We consider the Picard operators $\mathcal{P}_n$ and $\mathcal{P}_{n;r}$ in exponential weighted spaces. We give some elementary and approximation properties of these operators.
References:
[1] Becker, M., Kucharski, D., Nessel, R. J.: Global approximation theorems for the Szász-Mirakyan operators in exponential weight spaces, in Linear Spaces and Approximation. Proc. Conf. Oberwolfach, 1977, Birkhäuser Verlag, Basel, 1978, pp. 319–333. MR 0499919
[2] Brown, B. M., Elliott, D., Paget, D. F.: Lipschitz constants for the Bernstein polynomials of Lipschitz continuous function. J. Approx. Theory 49 (1987), 196–199. DOI 10.1016/0021-9045(87)90087-6 | MR 0874953
[3] Butzer, P. L., Nessel, R. J.: Fourier Analysis and Approximation. vol. 1, Birkhäuser Verlag, Basel und Stuttgart, 1971. MR 0510857 | Zbl 0217.42603
[4] De Vore, R. A., Lorentz, G. G.: Constructive Approximation. Springer-Verlag, Berlin, 1993. MR 1261635
[5] Deeba, E., Mohapatra, R. N., Rodriguez, R. S.: On the degree of approximation of some singular integrals. Rend. Mat. Appl. (7) (1988), 345–355. MR 1012098 | Zbl 0677.42015
[6] Ditzian, Z., Totik, V.: Moduli of Smoothness. Springer-Verlag, New-York, 1987. MR 0914149 | Zbl 0666.41001
[7] Khan, A.: On the degree of approximation of K. Picard and E. Poisson - Cauchy singular integrals. Rend. Mat. Appl. (7) (1982), 123–128. MR 0663719 | Zbl 0501.42009
[8] Khan, M. K., Vecchia, B. D., Fassih, A.: On the monotonicity of positive linear operators. J. Approx. Theory 92 (1998), 22–37. DOI 10.1006/jath.1996.3113 | MR 1492856 | Zbl 0898.41019
[9] Kirov, G. H.: A generalization of the Bernstein polynomials. Math. Balkanica (N.S.) 2 (2) (1992), 147–153. MR 1182946 | Zbl 0838.41017
[10] Leśniewicz, A., Rempulska, L., Wasiak, J.: Approximation properties of the Picard singular integral in exponential weight spaces. Publ. Mat. 40 (2) (1996), 233–242. MR 1425617
[11] Mohapatra, R. N., Rodriguez, R. S.: On the rate of convergence of singular integrals for Hölder continuous functions. Math. Nachr. 149 (1990), 117–124. DOI 10.1002/mana.19901490108 | MR 1124797 | Zbl 0726.42003
[12] Rempulska, L., Walczak, Z.: On modified Picard and Gauss - Weierstrass singular integrals. Ukrain. Math. Zh. 57 (11) (2005), 1577–1584. MR 2221659 | Zbl 1097.42009
[13] Timan, A. F.: Theory of Approximation of Functions of a Real Variable. Moscow, 1960, (Russian). MR 0117478
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