Balázs–Shepard Operators on Infinite Intervals, II
✍ Scribed by G Mastroianni; J Szabados
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 248 KB
- Volume
- 90
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
The weighted uniform convergence of the Bala zs Shepard operator is considered on the real line. As a consequence of the main result, it is proved that for a wide class of weights, rational functions are always dense in the space of continuous functions, in contrast to the polynomials where the Akhiezer Babenko condition is necessary for such density.
1997 Academic Press
In the convergence of the so-called Bala zs Shepard operators
(1) was considered on R. Here
are equidistant nodes where * n >0 is a real number depending on n. In the case where f(x) has equal finite limits at \ the error estimates obtained in [1] were quite satisfactory, but when f (x) is unbounded at \ we could not get results for the original operator, only for some modification. The purpose of this paper is to settle the problem of weighted approximation by the Bala zs Shepard operators.
To do so we must define our weight function w(x)=e &Q(x) by the following properties: There exists an a 0 such that (i) Q(x) is even, lim x Ä Q(x)= ; article no. AT963075 1