Ostrovska, SofiyaOstrovska, SMathematics2024-07-052024-07-052006380021-90451096-043010.1016/j.jat.2005.09.0152-s2.0-31144465102https://doi.org/10.1016/j.jat.2005.09.015https://hdl.handle.net/20.500.14411/1170Let B-n(f, q; x), n = 1, 2,... be the q-Bernstein polynomials of a function f is an element of C[0, 1]. In the case 0 < q < 1, a sequence {B-n(f, q; x)} generates a positive linear operator B-infinity = B-infinity,B-q on C[0, 1], which is called the limit q-Bernstein operator In this paper, a connection between the smoothness of a function f and the analytic properties of its image under Boo is studied. (c) 2005 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessq-Bemstein polynomialsq-binomial coefficientslimit q-Bernstein operatorpositive operatoranalytic continuationentire functiongrowth estimatesmodulus of continuityArticleQ213813753WOS:000235314600002