Ostrovska, SofiyaMathematics2024-07-052024-07-0520160139-99181337-221110.1515/ms-2015-01162-s2.0-84969706134https://doi.org/10.1515/ms-2015-0116https://hdl.handle.net/20.500.14411/484The q-Bernstein basis used to construct the q-Bernstein polynomials is an extension of the Bernstein basis related to the q-binomial probability distribution. This distribution plays a profound role in the q-boson operator calculus. In the case q > 1, q-Bernstein basic polynomials on [0, 1] combine the fast increase in magnitude with sign oscillations. This seriously complicates the study of q-Bernstein polynomials in the case of q > 1. The aim of this paper is to present new results related to the q-Bernstein polynomials B-n,B- q of discontinuous functions in the case q > 1. The behavior of polynomials B-n,B- q(f; x) for functions f possessing a logarithmic singularity at 0 has been examined. (C) 2016 Mathematical Institute Slovak Academy of Scienceseninfo:eu-repo/semantics/closedAccessq-integersq-binomial coefficientsq-Bernstein polynomialsconvergenceArticleQ16617378WOS:0003757455000072