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Let Bm(f) be the Bernstein polynomial of degree m. The Generalized Bernstein polynomials B m,λ (f, x) = ∞ ∑ i=1 (−1) i+1 (λ i) B i m (f ; x), λ ∈ R + were introduced in [13]. In the present paper some of their properties are revisited and some applications are presented. Indeed, the stability and the convergence of a quadrature rule on equally spaced knots… (More)

- D Occorsio, M G Russo
- 2015

The one dimensional Generalized Bernstein Operator B m,s (shortly GB operator) was introduced in [3] (see also [4]) on the space of continuous functions in [0, 1] and defined as follows

Let {p m (w α)} m be the sequence of the polynomials orthonormal w.r.t. the Sonin-Markov weight w α (x) = e −x 2 |x| α. The authors study extended Lagrange interpolation processes essentially based on the zeros of p m (w α)p m+1 (w α), determining the conditions under which the Lebesgue constants, in some weighted uniform spaces, are optimal.

- D Occorsio, M G Russo
- 2011

In [1] it was proved that if w(x) = e −x β x γ , γ ≥ −1, β > 1 2 , is a generalized Laguerre weight and ¯ w(x) = xw(x), then the zeros of the orthonormal polynomial p m+1 (w) interlace with those of p m (¯ w). Hence it is possible to consider an extended Lagrange interpolation process based on the zeros of p m+1 (w)p m (¯ w). In this talk the named… (More)

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