Ostrovska, SofiyaMathematics2024-10-062024-10-0620101068-9613https://hdl.handle.net/20.500.14411/8793Since for q > 1, the q-Bernstein polynomials B(n,q) are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. In this paper, new results on the approximation of continuous functions by the q-Bernstein polynomials in the case q > 1 are presented. It is shown that if f is an element of C[0, 1] and admits an analytic continuation f(z) into {z : |z| < a}, then B(n,q) (f; z) -> f (z) as n -> infinity, uniformly on any compact set in {z : |z| < a}.eninfo:eu-repo/semantics/closedAccessq-integersq-binomial coefficientsq-Bernstein polynomialsuniform convergenceArticleQ3Q337105112WOS:0002859767000067