Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus

Details Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus

2004-10-07

arxiv.org/abs/math/0410206v2

Mathematics

Functional Analysis

Scientific paper

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, shape-preserving property, Voronovskaya theorem, self-adjointness. Some properties of the eigenvectors, which are $q$-extensions of Jacobi polynomials, are given.

Affiliated with

Also associated with

No associations

Rating

Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-216765