On the convergence of a truncated class of operators

Abstract

In this paper we are dealing with a general class of positive approximation processes of discrete type expressed in series. We modify them into finite sums and investigate their approximation properties in weighted spaces of continuous  functions. Some special cases are also revealed.

Authors

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

Keywords

Linear positive operators, Bohman-Korovkin test functions, rate of convergence, weight spaces.

Paper coordinates

O. Agratini, On the convergence of a truncated class of operators, Bulletin of the Institute of Mathematics Academia Sinica, 31 (2003) no. 3, pp. 213-223.

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About this paper

Journal

Bulletin of the Institute of Mathematics Academia Sinica

Publisher Name
DOI
Print ISSN

2304-7909

Online ISSN

2304-7895

google scholar link

1. O. Agratini, Smoothness properties of positive summation integral operators, East Journal on Approximations, 5(4) (1999), 381-392.
2. F. Altomare and M. Campiti, Korovkin-type Approximation Theory and its Applications, de Gruyter Series Studies in Mathematics, Vol.17, Walter de Gruyter & Co., Berlin, New York, 1994.
3. Z. Ditzian and V. Totik, Moduli of Smoothness, Springer Series in Computational Mathematics, Vol.9, Berlin, 1987.
4. J. Grof, Approximation durch Polynome mit Belegfunktionen, Acta Math. Acad. Sci. Hungar., 35(1980), 109-116.
5. H.-G. Lehnhoff, On a modified Sz´asz-Mirakjan operator, J. Approx. Theory, 42(1984), 278-282.
6. J. Wang and S. Zhou, On the convergence of modified Baskakov operators, Bull. Inst. Math. Academia Sinica, 28(2) (2000), 117-123.
7. G. Z. Zhou and S. P. Zhou, A remark on a modified Szasz-Mirakjan operator, Colloq. Math., 79(1999), 157-160.

2003

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