We introduce polynomials Bni(x;ω|q), depending on two parameters q and ω, which generalize classical Bernstein polynomials, discrete Bernstein polynomials defined by Sablonnière, as well as q-Bernstein polynomials introduced by Phillips. Basic properties of the new polynomials are given. Also, formulas relating Bni(x;ω|q), big q-Jacobi and q-Hahn (or dual q-Hahn) polynomials are presented.
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