Gurel, OvguOstrovska, SofiyaTuran, Mehmet2026-02-052026-02-0520261660-54461660-545410.1007/s00009-025-03042-72-s2.0-105027030397https://doi.org/10.1007/s00009-025-03042-7https://hdl.handle.net/20.500.14411/11131Ostrovska, Sofiya/0000-0003-1842-7953; Turan, Mehmet/0000-0002-1718-3902In the study of various q-versions of the Bernstein polynomials, a significant attention is paid to their limit operators. The present work focuses on the impact of the limit q-Stancu operator Sq infinity,alpha on the analytic properties of functions when 0 < q < 1 and alpha > 0. It is shown that for every f is an element of C[0, 1], the function S-q,(alpha infinity)fadmits an analytic continuation into the disk {z : z+alpha/(1-q) < 1+ alpha/(1-q)}. In addition, it is proved that the more derivatives f has at x = 1, the wider this disk becomes. Further, if f is infinitely differentiable at x = 1, then the function S-q,(alpha infinity)fis entire. Finally, some growth estimates for (S-q,(alpha infinity)f)(z) are obtained.eninfo:eu-repo/semantics/openAccessQ-Bernstein OperatorQ-Stancu OperatorAnalytic FunctionGrowth EstimateArticle