A note on the modified \(q\)-Bernstein polynomials. (English) Zbl 1198.33005

Summary: We propose the modified \(q\)-Bernstein polynomials of degree \(n\) which are different \(q\)-Bernstein polynomials of G. M. Phillips [Ann. Numer. Math. 4, No. 1-4, 511–518 (1997; Zbl 0881.41008)]. From these modified \(q\)-Bernstein polynomials of degree \(n\), we derive some recurrence formulae for the modified \(q\)-Bernstein polynomials.


33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
11B65 Binomial coefficients; factorials; \(q\)-identities
05A30 \(q\)-calculus and related topics
41A10 Approximation by polynomials


Zbl 0881.41008
Full Text: DOI arXiv EuDML


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