Asymptotic formulae for recursively defined Baskakov-type operators

Abstract


We deal with Baskakov-type operators which are defined by replacing the binomial coeffcients with general ones satisfying a recursively relation. We establish a Voronovskaja-type formula and also we give a global approximation property using some weighted norms.

Authors

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Baskakov-type operators, degree of approximation, Voronovskaja-type formula, weighted norms.

Paper coordinates

O. Agratini, Asymptotic formulae for recursively defined Baskakov-type operators, Publications de L’Institut Mathematique (Beograd) (NS), 63 (1998) no. 77, pp. 152-162.

PDF

About this paper

Journal
Publisher Name
DOI
Print ISSN
Online ISSN

google scholar link

[1] O. Agratini, Properties of a new class of recursively defined Baskakov-type operators, Archivum Mathematicum 33 (1997), to appear
[2] F. Altomare, Limit semigroups of Bernstein-Schnabl operators associated with positive projections, Ann. Sc. Norm. Sup. Pisa, Serie IV, (16)2 (1989), 259-279.
[3] F. Altomare, Positive projections approximation processes and degenerate di usion equations, Conf. Sem. Mat. Univ. Bari, 241 (1991), 43-68.
[4] F. Altomare, On some sequences of positive linear operators on unbounded intervals, in: Approximation and Optimization, Proceedings of ICAOR: International Conference on Approximation Theory and Optimization, Cluj-Napoca, July 29 { August 1, 1996, D.D. Stancu et al.Eds., Transilvania Press Cluj-Napoca, 1997, pp. 1-16.
[5] F. Altomare, M. Campiti, Korovkin-type Approximation Theory and its Applications, De Gruyter Studies in Mathematics, Vol. 17, De Gruyter, Berlin, New York, 1994.
[6] M.Becker, Global approximation theorems for Szasz-Mirakjan and Baskakov operators in polynomial weight spaces, Indiana Univ. Math. J. 27 (1978), 127-142.
[7] M Campiti, G. Metafune, Approximation properties of recursively defined Bernstein-type op- erators, J. Approx. Theory 87 (1996), 243-269.
[8] P.C. Sikkema, On some linear positive operators, Indagationes Mathematicae 32 (1970), 327-337.

1998

Related Posts