Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus
泛函分析
2007-05-23 v2
摘要
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the -Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in . Numerous properties of the modified Bernstein Polynomials are extended to their -analogues: simultaneous approximation, pointwise convergence even for unbounded functions, shape-preserving property, Voronovskaya theorem, self-adjointness. Some properties of the eigenvectors, which are -extensions of Jacobi polynomials, are given.
引用
@article{arxiv.math/0410206,
title = {Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus},
author = {Marie-Madeleine Derriennic},
journal= {arXiv preprint arXiv:math/0410206},
year = {2007}
}