Geodesic
Bernstein-type operators on the half line
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 851-860 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 41A10, 41A35, 41A36
Keywords: Bernstein-Chlodovsky operators; approximation process; Voronovskaja-type formula 
@article{CMJ_2002_52_4_a15,
     author = {Attalienti, Antonio and Campiti, Michele},
     title = {Bernstein-type operators on the half line},
     journal = {Czechoslovak Mathematical Journal},
     pages = {851--860},
     year = {2002},
     volume = {52},
     number = {4},
     mrnumber = {1940064},
     zbl = {1015.41014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a15/}
}
TY  - JOUR
AU  - Attalienti, Antonio
AU  - Campiti, Michele
TI  - Bernstein-type operators on the half line
JO  - Czechoslovak Mathematical Journal
PY  - 2002
SP  - 851
EP  - 860
VL  - 52
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a15/
LA  - en
ID  - CMJ_2002_52_4_a15
ER  - 
%0 Journal Article
%A Attalienti, Antonio
%A Campiti, Michele
%T Bernstein-type operators on the half line
%J Czechoslovak Mathematical Journal
%D 2002
%P 851-860
%V 52
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a15/
%G en
%F CMJ_2002_52_4_a15
Attalienti, Antonio; Campiti, Michele. Bernstein-type operators on the half line. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 851-860. http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a15/

[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

[2] F.  Altomare and E. M.  Mangino: On a generalization of Baskakov operators. Rev. Roumaine Math. Pures Appl. 44 (1999), 683–705. | MR

[3] F.  Altomare and E. M.  Mangino: On a class of elliptic-parabolic equations on unbounded intervals. Positivity 5 (2001), 239–257. | DOI | MR

[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

[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 | MR

[6] B.  Eisenberg: Another look at the Korovkin theorems. J.  Approx. Theory 17 (1976), 359–365. | DOI | MR | Zbl

[7] S. M.  Eisenberg: Korovkin’s theorems. Bull. Malaysian Math. Soc. 2 (1979), 13–29. | MR

[8] S.  Eisenberg and B.  Wood: Approximating unbounded functions by linear operators generated by moment sequences. Studia Math. 35 (1970), 299–304. | DOI | MR

[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

[10] A. D.  Gadzhiev: Theorems of Korovkin type. Math. Notes 20 (1976), 995–998. | DOI

[11] J. J.  Swetits and B.  Wood: Unbounded functions and positive linear operators. J.  Approx. Theory 34 (1982), 325–334. | DOI | MR

[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

[13] H. F.  Trotter: Approximation of semi-groups of operators. Pacific J.  Math. 8 (1958), 887–919. | DOI | MR | Zbl