A de Casteljau algorithm for \(q\)-Bernstein-Stancu polynomials. (English) Zbl 1209.33017

Summary: This paper is concerned with a generalization of \(q\)-Bernstein polynomials and Stancu operators, where the function is evaluated at intervals which are in geometric progression. It is shown that these polynomials can be generated by a de Casteljau algorithm, which is a generalization of that relating to the classical case and the \(q\)-Bernstein case.


33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
11B65 Binomial coefficients; factorials; \(q\)-identities
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