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The authors give a procedure to construct extended interpolation formulae and prove some uniform convergence theorems.

- Giuseppe Mastroianni, Donatella Occorsio
- J. Computational Applied Mathematics
- 2010

- Donatella Occorsio
- Applied Mathematics and Computation
- 2009

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Dedicated to Professor József Szabados on the occasion of his 70th birthday. a b s t r… (More)

- Giuseppe Mastroianni, Gradimir V. Milovanovic, Donatella Occorsio
- Applied Mathematics and Computation
- 2013

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)

- Donatella Occorsio, Maria Grazia Russo
- J. Computational Applied Mathematics
- 2014

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
- 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

- D. Occorsio
- 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)

- Donatella Occorsio
- Applied Mathematics and Computation
- 2011

- Donatella Occorsio, Maria Grazia Russo
- Applied Mathematics and Computation
- 2011

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