Ostrovska, SofiyaOzban, Ahmet YasarMathematics2024-07-052024-07-05201330096-30031873-564910.1016/j.amc.2013.07.0342-s2.0-84881433938https://doi.org/10.1016/j.amc.2013.07.034https://hdl.handle.net/20.500.14411/419The problem to describe the Bernstein polynomials of unbounded functions goes back to Lorentz. The aim of this paper is to investigate the convergence properties of the q-Bernstein polynomials B-n,B-q(f; x) of the Cauchy kernel 1/x-alpha with a pole alpha is an element of [0, 1] for q > 1. The previously obtained results allow one to describe these properties when a pole is different from q(-m) for some m is an element of {0, 1, 2, ...}. In this context, the focus of the paper is on the behavior of polynomials B-n,B-q(f; x) for the functions of the form f(m)(x) = 1/(x - q(-m)), x not equal q(-m) and f(m)(q(-m)) = a, a is an element of R. Here, the problem is examined both theoretically and numerically in detail. (C) 2013 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessq-Integersq-Bernstein polynomialsConvergenceApproximation of unbounded functionsCauchy kernelArticleQ1220735747WOS:000324558600070