Ostrovska, SofiyaMathematics2024-07-052024-07-0520131110-757X1687-004210.1155/2013/1597202-s2.0-84876580340https://doi.org/10.1155/2013/159720https://hdl.handle.net/20.500.14411/300The limit q-Bernstein operator B-q emerges naturally as a modification of the Szasz-Mirakyan operator related to the Euler distribution, which is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state. At the same time, this operator bears a significant role in the approximation theory as an exemplary model for the study of the convergence of the q-operators. Over the past years, the limit q-Bernstein operator has been studied widely from different perspectives. It has been shown that. is a positive shape-preserving linear operator on C[0, 1] with parallel to B-q parallel to = 1. Its approximation properties, probabilistic interpretation, the behavior of iterates, and the impact on the smoothness of a function have already been examined. In this paper, we present a review of the results on the limit q-Bernstein operator related to the approximation theory. A complete bibliography is supplied.eninfo:eu-repo/semantics/openAccess[No Keyword Available]ReviewQ2WOS:0003172112000015