On the <i>q</I>-bernstein Polynomials of the Logarithmic Function in the Case <i>q</I> > 1
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Date
2016
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Walter de Gruyter Gmbh
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Abstract
The q-Bernstein basis used to construct the q-Bernstein polynomials is an extension of the Bernstein basis related to the q-binomial probability distribution. This distribution plays a profound role in the q-boson operator calculus. In the case q > 1, q-Bernstein basic polynomials on [0, 1] combine the fast increase in magnitude with sign oscillations. This seriously complicates the study of q-Bernstein polynomials in the case of q > 1. The aim of this paper is to present new results related to the q-Bernstein polynomials B-n,B- q of discontinuous functions in the case q > 1. The behavior of polynomials B-n,B- q(f; x) for functions f possessing a logarithmic singularity at 0 has been examined. (C) 2016 Mathematical Institute Slovak Academy of Sciences
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q-integers, q-binomial coefficients, q-Bernstein polynomials, convergence
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Volume
66
Issue
1
Start Page
73
End Page
78