Ostrovska, SofiyaMathematics2024-07-052024-07-05200791017-139810.1007/s11075-007-9081-72-s2.0-34248364864https://doi.org/10.1007/s11075-007-9081-7https://hdl.handle.net/20.500.14411/936Since in the case q > 1, q-Bernstein polynomials are not positive linear operators on C[ 0, 1], the study of their approximation properties is essentially more difficult than that for 0 < q < 1. Despite the intensive research conducted in the area lately, the problem of describing the class of functions in C[ 0, 1] uniformly approximated by their q-Bernstein polynomials ( q > 1) remains open. It is known that the approximation occurs for functions admitting an analytic continuation into a disc {z : | z| < R}, R > 1. For functions without such an assumption, no general results on approximation are available. In this paper, it is shown that the function f ( x) = ln( x + a), a > 0, is uniformly approximated by its q-Bernstein polynomials ( q > 1) on the interval [ 0, 1] if and only if a >= 1.eninfo:eu-repo/semantics/closedAccessq-integersq-binomial coefficientsq-Bernstein polynomialsuniform convergenceArticleQ1Q14416982WOS:000246359200005