Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Bernstein-Chlodovsky operators; approximation process; Voronovskaja-type formula
Bernstein-Chlodovsky operators; approximation process; Voronovskaja-type formula
Summary:
We define Bernstein-type operators on the half line $\mathopen [0,+\infty \mathclose [$ by means of two sequences of strictly positive real numbers. After studying their approximation properties, we also establish a Voronovskaja-type result with respect to a suitable weighted norm.
References:
[1] F. Altomare and M. Campiti: Korovkin-type Approximation Theory and its Applications. Vol.17, de Gruyter Series Studies in Mathematics, de Gruyter, Berlin-New York, 1994. MR 1292247
[2] F. Altomare and E. M. Mangino: On a generalization of Baskakov operators. Rev. Roumaine Math. Pures Appl. 44 (1999), 683–705. MR 1839672
[3] F. Altomare and E. M. Mangino: On a class of elliptic-parabolic equations on unbounded intervals. Positivity 5 (2001), 239–257. DOI 10.1023/A:1011450903149 | MR 1836748
[4] I. Chlodovsky: Sur le développement des fonctions définies dans un interval infini en séries de polynômes de M. S. Bernstein. Compositio Math. 4 (1937), 380–393. MR 1556982
[5] Ph. Clément and C. A. Timmermans: On $C_0$-semigroups generated by differential operators satisfying Ventcel’s boundary conditions. Indag. Math. 89 (1986), 379–387. DOI 10.1016/1385-7258(86)90023-5 | MR 0869754
[6] B. Eisenberg: Another look at the Korovkin theorems. J. Approx. Theory 17 (1976), 359–365. DOI 10.1016/0021-9045(76)90080-0 | MR 0417644 | Zbl 0335.41012
[7] S. M. Eisenberg: Korovkin’s theorems. Bull. Malaysian Math. Soc. 2 (1979), 13–29. MR 0545798
[8] S. Eisenberg and B. Wood: Approximating unbounded functions by linear operators generated by moment sequences. Studia Math. 35 (1970), 299–304. DOI 10.4064/sm-35-3-299-304 | MR 0271585
[9] A. D. Gadzhiev: The convergence problem for a sequence of positive linear operators on unbounded sets, and theorems analogous to that of P. P. Korovkin. Soviet. Math. Dokl. 15 (1974), 1433–1436. Zbl 0312.41013
[10] A. D. Gadzhiev: Theorems of Korovkin type. Math. Notes 20 (1976), 995–998. DOI 10.1007/BF01146928
[11] J. J. Swetits and B. Wood: Unbounded functions and positive linear operators. J. Approx. Theory 34 (1982), 325–334. DOI 10.1016/0021-9045(82)90075-2 | MR 0656633
[12] C. A. Timmermans: On $C_0$-semigroups in a space of bounded continuous functions in the case of entrance or natural boundary points. In: Approximation and Optimization. Lecture Notes in Math. 1354, J. A. Gómez Fernández et al. (eds.), Springer-Verlag, Berlin-New York, 1988, pp. 209–216. MR 0996675
[13] H. F. Trotter: Approximation of semi-groups of operators. Pacific J. Math. 8 (1958), 887–919. DOI 10.2140/pjm.1958.8.887 | MR 0103420 | Zbl 0099.10302
Search
Partner of
