Some identities for the operator of Bleimann, Butzer and Hahn involving divided differences

Calcolo

Volumn 36, Issue 3, 1999, Pages 143-160

  Abel, Ulrich ^a   Ivan, Mircea ^b  

^a UNIVERSITY OF APPLIED SCIENCES   (Germany)

^b TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION PROCESS; BERNSTEIN OPERATOR; DIFFERENCE OPERATORS; DIVIDED DIFFERENCE; HIGH-ORDER; HIGHER-ORDER; LINEAR OPERATORS; NEW RESULTS; PROPERTY; SIMULTANEOUS APPROXIMATION;

MATHEMATICAL OPERATORS;

EID: 13444264403     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100920050028     Document Type: Article

References (23)

1. Abel, U.: On the asymptotic approximation with operators of Bleimann, Butzer and Hahn. Indag. Math. (N.S.) 7, 1-9 (1996)
2. Abel, U.: On the asymptotic approximation with bivariate operators of Bleimann, Butzer and Hahn. J. Approx. Theory 97, 181-198 (1999)
3. Adell, J.A., Badía, F.G., de la Cal, J.: On the iterates of some Bernstein-type operators. J. Math. Anal. Appl. 209, 529-541 (1997)
4. Agratini, O.: An application of divided differences. Automat. Comput. Appl. Math. 4, 95-99 (1995)
5. Arama, O.: Properties concerning the monotonicity of the sequence of interpolation polynomials of S. N. Bernstein and their application to the study of the approximation of functions. (Romanian French summary) Acad. R.P. Romîne. Fil. Cluj. Stud. Cerc. Mat. 8, 195-210 (1957)
6. Bleimann, G., Butzer, P.L., Hahn, L.: A Bernstein-type operator approximating continuous functions on the semi-axis. Nederl. Akad. Wetensch. Indag. Math. 42, 255-262 (1980)
7. Della Vecchia, B.: Some properties of a rational operator of Bernstein-type. In: Nevai, P., Pinkus, A. (eds.): Progress in approximation theory. Boston: Academic Press 1991, pp. 177-185
8. DeVore, R.A., Lorentz, G.G.: Constructive approximation. Berlin: Springer 1993
9. Ivan, M.: A note on the Bleimann-Butzer-Hahn operator. Automat. Comput. Appl. Math. 6, 11-15 (1997)
10. Jayasri, C., Sitamaran, Y.: Direct and inverse theorems for certain Bernstein-type operators. Indian J. Pure Appl. Math. 16, 1495-1511 (1985)
11. Jayasri, C., Sitamaran, Y.: On a Bernstein-type operator of Bleimann, Butzer and Hahn. J. Comput. Appl. Math. 47, 267-272 (1993)
12. Jayasri, C., Sitamaran, Y.: On a Bernstein-type operator of Bleimann, Butzer and Hahn. II. J. Anal. 1, 125-137 (1993)
13. Karlin, S.: Total positivity. Stanford: Stanford Univ. Press 1968
14. Khan, R.A.: A note on a Bernstein-type operator of Bleimann, Butzer and Hahn. J. Approx. Theory 53, 295-303 (1988)
15. Khan, R.A.: Some properties of a Bernstein-type operator of Bleimann, Butzer and Hahn. In: Nevai, P., Pinkus, A. (eds.): Progress in approximation theory. Boston: Academic Press 1991, pp. 497-504
16. Mercer, A.McD.: A Bernstein-type operator approximating continuous functions on the half-line. Bull. Calcutta Math. Soc. 81, 133-137 (1989)
17. Schoenberg, I.J.: On variation diminishing approximation methods. In: Langer, R.E. (ed.): On numerical approximation. Madison: Univ. of Wisconsin Press 1959, pp. 249-274
18. Stancu, D.D.: The remainder of certain linear approximation formulas in two variables. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 1, 137-163 (1964)
19. Stancu, D.D.: On the monotonicity of the sequence formed by the first order derivatives of the Bernstein polynomials. Math. Z. 98, 46-51 (1967)
20. Stancu, D.D.: Application of divided differences to the study of monotonicity of the derivatives of the sequence of Bernstein polynomials. Calcolo 16, 431-445 (1979)
21. Stancu, D.D.: On the representation by divided differences of the remainder in Bernstein's approximation formula. Seminar of numerical and statistical calculus (Preprint 85-4). University of Cluj-Napoca Research Seminars 1985, 103-110
22. Temple, W.B.: Stieltjes integral representation of convex functions. Duke Math. J. 21, 527-531 (1954)
23. Totik, V.: Uniform approximation by Bernstein-type operators. Nederl. Akad. Wetensch. Indag. Math. 46, 87-93 (1984)