Ostrovska, SofiyaOstrovska, SofiyaMathematics2024-10-062024-10-06200821331-4343[WOS-DOI-BELIRLENECEK-535]https://hdl.handle.net/20.500.14411/8803Since for q > 1. q-Bernstein polynomials 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. It is known that, in the case q > 1. the q-Bernstein polynomials approximate the entire functions and, in particular, polynomials uniformly on any compact set in C. In this paper. the possibility of the approximation for the function (z + a)(alpha), a >= 0. with a non-integer alpha > -1 is studied. It is proved that for a > 0, the function is uniformly approximated on any compact set in {z : vertical bar z vertical bar < a}, while on any Jordan arc in {z : vertical bar z vertical bar > a}. the uniform approximation is impossible, In the case a = 0(1) the results of the paper reveal the following interesting phenomenon: the power function z(alpha), alpha > 0: is approximated by its, q-Bernstein polynomials either on any (when alpha is an element of N) or no (when alpha is not an element of N) Jordan arc in C.eninfo:eu-repo/semantics/closedAccessq-integersq-binomial coefficientsq-Bernstein polynomialsuniform convergenceArticleQ2Q2113585597WOS:000257877600019