Ostrovska,S.Mathematics2024-10-062024-10-0620101068-96132-s2.0-77955425049https://hdl.handle.net/20.500.14411/9246Since for q > 1, the q-Bernstein polynomials Bn,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 Ε C[0, 1] and admits an analytic continuation f(z) into {z : |z| < a}, then Bn,q (f; z) → f(z) as n → λ, uniformly on any compact set in {z : |z| < a}. Copyright © 2010, Kent State University.eninfo:eu-repo/semantics/closedAccessQ-Bernstein polynomialsQ-binomial coefficientsQ-integersUniform convergenceArticleQ3Q3371051127