Abstract
We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove some direct approximation theorems for functions f such that w σ f ∈ L p(R), where 1 ≤ p ≤ ∞ and w σ(x) = exp(−σx 2), σ > 0.
[1] BECKER, M.— BUTZER, P. L.— NESSEL, R. J.: Saturation for Favard operators in weighted function spaces, Studia Math. 59 (1976), 139–153. 10.4064/sm-59-2-139-153Search in Google Scholar
[2] BECKER, M.: Inverse theorems for Favard operators in polynomial weight spaces, Ann. Soc. Math. Polon. Ser. I: Comment. Math. 22 (1981), 165–173. Search in Google Scholar
[3] BUTZER, P. L.— NESSEL, R. J.: Fourier Analysis and Approximation, Vol. I, Academic Press, New York-London, 1971. 10.1007/978-3-0348-7448-9Search in Google Scholar
[4] FAVARD, J.: Sur les multiplicateurs d’interpolation, J. Math. Pures Appl. 23 (1944), 219–247. Search in Google Scholar
[5] GAWRONSKI, W.— STADTM-ULLER, U.: Approximation of continuous functions by generalized Favard operators, J. Approx. Theory 34 (1982), 384–396. http://dx.doi.org/10.1016/0021-9045(82)90081-810.1016/0021-9045(82)90081-8Search in Google Scholar
[6] NOWAK, G.— PYCH-TABERSKA, P.: Approximation properties of the generalized Favard-Kantorovich operators, Ann. Soc. Math. Polon. Ser. I: Comment.Math. 39 (1999), 139–152. Search in Google Scholar
[7] NOWAK, G.— PYCH-TABERSKA, P.: Some properties of the generalized Favard-Durrmeyer operators, Funct. Approx. Comment. Math. 29 (2001), 103–112. 10.7169/facm/1538186721Search in Google Scholar
[8] PYCH-TABERSKA, P.: On the generalized Favard operators, Funct. Approx. Comment. Math. 26 (1988), 265–273. Search in Google Scholar
© 2010 Mathematical Institute, Slovak Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
