Generalized Bernstein polynomials with Pollaczek weight
- Della Vecchia, B.
- Mastroianni, G.
- Szabados, J.
DOIAbstract
AbstractBernstein polynomials are a useful tool for approximating functions. In this paper, we extend the applicability of this operator to a certain class of locally continuous functions. To do so, we consider the Pollaczek weight w(x)≔exp(−1x(1−x)),0<x<1, which is rapidly decaying at the endpoints of the interval considered. In order to establish convergence theorems and error estimates, we need to introduce corresponding moduli of smoothness and K-functionals. Because of the unusual nature of this weight, we have to overcome a number of technical difficulties, but the equivalence of the moduli and K-functionals is a benefit interesting in itself. Similar investigations have been made in [B. Della Vecchia, G. Mastroianni, J. Szabados, Wei...
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