# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
The saturation of convergence on the interval [0,1] for the $q$-Bernstein polynomials in the case $q>1$. (English) Zbl 1236.41011
Summary: We consider saturation of convergence on the interval $\left[0,1\right]$ for the $q$-Bernstein polynomials of a continuous function $f$ for arbitrary fixed $q>1$. We show that the rate of uniform convergence on $\left[0,1\right]$ is $o\left({q}^{-n}\right)$ if and only if $f$ is linear. The result is sharp in the following sense: it ceases to be true if we replace “$o$” by “$O$”.
##### MSC:
 41A10 Approximation by polynomials 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)