Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus
نویسنده
چکیده
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, pointwise convergence even for unbounded functions, shapepreserving property, Voronovskaya theorem, self-adjointness. Some properties of the eigenvectors, which are q-extensions of Jacobi polynomials, are given.
منابع مشابه
Modified Berstein Polynomials and Jacobi Polynomials in q-Calculus
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...
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