Gurel, OvguOstrovska, SofiyaTuran, MehmetMathematics2024-11-052024-11-0520240139-99181337-221110.1515/ms-2024-00922-s2.0-85207277022https://doi.org/10.1515/ms-2024-0092https://hdl.handle.net/20.500.14411/10243The q-Durrmeyer polynomials are one of the popular q-versions of the classical operators of approximation theory. They have been studied from different points of view by a number of researchers. The aim of this work is to estimate the rate of convergence for the sequence of the q-Durrmeyer polynomials in the case 0 < q < 1. It is proved that for any compact set D subset of C, the rate of convergence is O(q(n)) as n -> infinity. The sharpness of the obtained result is demonstrated.eninfo:eu-repo/semantics/closedAccessq-integersq-Durrmeyer operatorlimit q-Durrmeyer operatorrate of convergenceanalytic functionArticleQ1Q274512671276WOS:001334471700014