Geodesic
On the approximation of analytic functions by the \(q\)-Bernstein polynomials in the case \(q>1\)
Electronic transactions on numerical analysis, Tome 37 (2010), pp. 105-112
Since for q > 1, the q-Bernstein polynomials B are not positive linear operators on C[0, 1], the n,q investigation of their convergence properties turns out to be much more difficult than that in the case 0 q 1. In this paper, new results on the approximation of continuous functions by the q-Bernstein polynomials in the case q > 1 are presented. It is shown that if f $\in $C[0, 1] and admits an analytic continuation f (z) into z : |z| a, then B (f ; z) $\rightarrow f$ (z) as n $\rightarrow \infty $, uniformly on any compact set in z : |z| a.n,q
Classification : 41A10, 30E10
Keywords: q-integers, q-binomial coefficients, q-Bernstein polynomials, uniform convergence 
@article{ETNA_2010__37__a20,
     author = {Ostrovska,  Sofiya},
     title = {On the approximation of analytic functions by the {\(q\)-Bernstein} polynomials in the case \(q>1\)},
     journal = {Electronic transactions on numerical analysis},
     pages = {105--112},
     year = {2010},
     volume = {37},
     zbl = {1207.41004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__37__a20/}
}
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Ostrovska,  Sofiya. On the approximation of analytic functions by the \(q\)-Bernstein polynomials in the case \(q>1\). Electronic transactions on numerical analysis, Tome 37 (2010), pp. 105-112. http://geodesic.mathdoc.fr/item/ETNA_2010__37__a20/