Geodesic
On some properties of the Picard operators
Archivum mathematicum, Tome 45 (2009) no. 2, pp. 125-135 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 41A25, 41A35
Keywords: Picard operator; exponential weighted space; degree of approximation; Voronovskaya type theorem 
@article{ARM_2009_45_2_a5,
     author = {Rempulska, Lucyna and Tomczak, Karolina},
     title = {On some properties of the {Picard} operators},
     journal = {Archivum mathematicum},
     pages = {125--135},
     year = {2009},
     volume = {45},
     number = {2},
     mrnumber = {2591669},
     zbl = {1212.41055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2009_45_2_a5/}
}
TY  - JOUR
AU  - Rempulska, Lucyna
AU  - Tomczak, Karolina
TI  - On some properties of the Picard operators
JO  - Archivum mathematicum
PY  - 2009
SP  - 125
EP  - 135
VL  - 45
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ARM_2009_45_2_a5/
LA  - en
ID  - ARM_2009_45_2_a5
ER  - 
%0 Journal Article
%A Rempulska, Lucyna
%A Tomczak, Karolina
%T On some properties of the Picard operators
%J Archivum mathematicum
%D 2009
%P 125-135
%V 45
%N 2
%U http://geodesic.mathdoc.fr/item/ARM_2009_45_2_a5/
%G en
%F ARM_2009_45_2_a5
Rempulska, Lucyna; Tomczak, Karolina. On some properties of the Picard operators. Archivum mathematicum, Tome 45 (2009) no. 2, pp. 125-135. http://geodesic.mathdoc.fr/item/ARM_2009_45_2_a5/

[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

[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 | MR

[3] Butzer, P. L., Nessel, R. J.: Fourier Analysis and Approximation. vol. 1, Birkhäuser Verlag, Basel und Stuttgart, 1971. | MR | Zbl

[4] De Vore, R. A., Lorentz, G. G.: Constructive Approximation. Springer-Verlag, Berlin, 1993. | MR

[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 | Zbl

[6] Ditzian, Z., Totik, V.: Moduli of Smoothness. Springer-Verlag, New-York, 1987. | MR | Zbl

[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 | Zbl

[8] Khan, M. K., Vecchia, B. D., Fassih, A.: On the monotonicity of positive linear operators. J. Approx. Theory 92 (1998), 22–37. | DOI | MR | Zbl

[9] Kirov, G. H.: A generalization of the Bernstein polynomials. Math. Balkanica (N.S.) 2 (2) (1992), 147–153. | MR | Zbl

[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

[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 | MR | Zbl

[12] Rempulska, L., Walczak, Z.: On modified Picard and Gauss - Weierstrass singular integrals. Ukrain. Math. Zh. 57 (11) (2005), 1577–1584. | MR | Zbl

[13] Timan, A. F.: Theory of Approximation of Functions of a Real Variable. Moscow, 1960, (Russian). | MR