Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus

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dc.creatorDerriennic, Marie-Madeleine
dc.date2004-10-07
dc.date2004-10-22
dc.date.accessioned2026-07-07T05:13:03Z
dc.date.available2026-07-07T05:13:03Z
dc.descriptionWe 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, shape-preserving property, Voronovskaya theorem, self-adjointness. Some properties of the eigenvectors, which are $q$-extensions of Jacobi polynomials, are given.
dc.identifierhttps://arxiv.org/abs/math/0410206
dc.identifierhttp://arxiv.org/abs/math/0410206
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72803
dc.subjectFunctional Analysis
dc.subject41A10; 41A25; 41A36
dc.titleModified Bernstein Polynomials and Jacobi Polynomials in q-Calculus
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