Previous |  Up |  Next


Baskakov-type operators; order of approximation; modulus of continuity
By starting from a recent paper by Campiti and Metafune [7], we consider a generalization of the Baskakov operators, which is introduced by replacing the binomial coefficients with other coefficients defined recursively by means of two fixed sequences of real numbers. In this paper, we indicate some of their properties, including a decomposition into an expression which depends linearly on the fixed sequences and an estimation of the corresponding order of approximation, in terms of the modulus of continuity.
[1] Agratini O.: Construction of Baskakov-type operators by wavelets. Rev. d’Analyse Num. et de Théorie de l’Approx., tome 26(1997), 3-10. MR 1703913 | Zbl 1039.42028
[2] Altomare F.: Positive projections approximation processes and degenerate diffusion equations. Conf. Sem. Mat. Univ. Bari, 241(1991), 43-68. MR 1185556 | Zbl 0789.47030
[3] Altomare F., Campiti M.: Korovkin-type Approximation Theory and its Applications. de Gruyter Studies in Mathematics, Vol. 17, de Gruyter, Berlin/New-York, 1994. MR 1292247 | Zbl 0924.41001
[4] Altomare F., Romanelli S.: On some classes of Lototsky-Schnabl operators. Note Mat., 12(1992), 1-13. MR 1258559 | Zbl 0811.47033
[5] Baskakov V. A.: An example of a sequence of linear positive operators in the space of continuous functions. Dokl. Akad. Nauk SSSR, 113(1957), 249-251 (in Russian). MR 0094640
[6] Campiti M.: Limit semigroups of Stancu-Mühlbach operators associated with positive projections. Ann. Sc. Norm. Sup. Pisa, Cl. Sci., 19(1992), 4, 51-67. MR 1183757 | Zbl 0784.47040
[7] Campiti M., Metafune G.: Approximation properties of recursively defined Bernstein-type operators. Journal of Approx. Theory, 87(1996), 243-269. MR 1420333 | Zbl 0865.41027
[8] Campiti M., Metafune G.: Evolution equations associated with recursively defined Bernstein-type operators. Journal of Approx. Theory, 87(1996), 270-290. MR 1420334 | Zbl 0874.41010
[9] Stancu D. D.: Two classes of positive linear operators. Analele Univ. Timişoara, Ser. St. Matem. 8(1970), 213-220. MR 0333538 | Zbl 0276.41009
[10] Stancu D. D. : Approximation of functions by means of some new classes of positive linear operators. in “Numerische Methoden der Approximations Theorie”, Vol. 1 (Proc. Conf. Math. Res. Inst., Oberwolfach, 1971; eds. L. Collatz, G. Meinardus), 187-203, Basel: Birkhäuser, 1972. MR 0380207
Partner of
EuDML logo