Ostrovska, SofiyaMathematics2024-07-052024-07-05200831422-63831420-901210.1007/s00025-008-0288-22-s2.0-49549115731https://doi.org/10.1007/s00025-008-0288-2https://hdl.handle.net/20.500.14411/1046Since for q > 1, the q-Bernstein polynomials B-n,B-q(f;.) are not positive linear operators on C[0, 1], their convergence properties are not similar to those in the case 0 < q = 1. It has been known that, in general, B-n,B-qn(f;.) does not approximate f is an element of C[0, 1] if q(n) -> 1(+), n ->infinity, unlike in the case q(n) -> 1(-). In this paper, it is shown that if 0 <= q(n) - 1 = o(n(-1)3(-n)), n -> infinity, then for any f is an element of C[0, 1], we have: B-n,B-qn(f; x) -> f(x) as n -> infinity, uniformly on [ 0,1].eninfo:eu-repo/semantics/closedAccessq-Bernstein polynomialsq-integersuniform convergencemaximum modulus principleArticleQ1Q3521-2179186WOS:000258456800014