No CrossRef data available.
Article contents
The r-monotonicity of generalized Bernstein polynomials
Published online by Cambridge University Press: 26 July 2012
Abstract
Let f ∊ C[0, 1] and let the Bn(f, q; x) be generalized Bernstein polynomials based on the q-integers that were introduced by Phillips. We prove that if f is r-monotone, then Bn(f, q; x) is r-monotone, generalizing well-known results when q = 1 and the results when r = 1 and r = 2 by Goodman et al. We also prove a sufficient condition for a continuous function to be r-monotone.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 3 , October 2012 , pp. 797 - 807
- Copyright
- Copyright © Edinburgh Mathematical Society 2012