Geodesic
The sharpness of convergence results for $q$-Bernstein polynomials in the case $q>1$
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1195-1206 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Due to the fact that in the case $q>1$ the $q$-Bernstein polynomials are no longer positive linear operators on $C[0,1],$ the study of their convergence properties turns out to be essentially more difficult than that for $q1.$ In this paper, new saturation theorems related to the convergence of $q$-Bernstein polynomials in the case $q>1$ are proved.
Due to the fact that in the case $q>1$ the $q$-Bernstein polynomials are no longer positive linear operators on $C[0,1],$ the study of their convergence properties turns out to be essentially more difficult than that for $q1.$ In this paper, new saturation theorems related to the convergence of $q$-Bernstein polynomials in the case $q>1$ are proved.
Classification : 30E10, 33D45, 41A10
Keywords: $q$-integers; $q$-binomial coefficients; $q$-Bernstein polynomials; uniform convergence; analytic function; Cauchy estimates 
@article{CMJ_2008_58_4_a23,
     author = {Ostrovska, Sofiya},
     title = {The sharpness of convergence results for $q${-Bernstein} polynomials in the case $q>1$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1195--1206},
     year = {2008},
     volume = {58},
     number = {4},
     mrnumber = {2471176},
     zbl = {1174.41010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a23/}
}
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Ostrovska, Sofiya. The sharpness of convergence results for $q$-Bernstein polynomials in the case $q>1$. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1195-1206. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a23/