Ostrovska, SofiyaMathematics2024-07-052024-07-0520060035-759610.1216/rmjm/11810693862-s2.0-33846826629https://doi.org/10.1216/rmjm/1181069386https://hdl.handle.net/20.500.14411/1175Let R-n(f,q;x) : C[0, 1] -> C[0, 1] be q-analogues of the Bernstein operators defined by Lupas in 1987. If q = 1, then R-n (f, 1; x) are classical Bernstein polynomials. For q not equal 1, the operators R-n (f, q; x) are rational functions rather than polynomials. The paper deals with convergence properties of the sequence {R-n (f, q; x)}. It is proved that {R-n (f, q(n); x)} converges uniformly to f(x) for any f(x) is an element of C[0, 1] if and only if q(n) -> 1. In the case q > 0, q not equal 1 being fixed the sequence I R. (f, q; x) I converges uniformly to f(x) is an element of C[0, 1] if and only if f(x) is linear.eninfo:eu-repo/semantics/openAccessBernstein polynomialsq-integersq-binomial coefficientsconvergenceArticleQ336516151629WOS:00024357990001468