Ostrovska, SofiyaOzban, Ahmet YasarMathematics2024-07-052024-07-05201470022-247X1096-081310.1016/j.jmaa.2013.12.0092-s2.0-84895905602https://doi.org/10.1016/j.jmaa.2013.12.009https://hdl.handle.net/20.500.14411/242The paper aims to investigate the convergence of the q-Bernstein polynomials B-n,B-q(f; x) attached to rational functions in the case q > 1. The problem reduces to that for the partial fractions (x - alpha)(-J), j is an element of N. The already available results deal with cases, where either the pole a is simple or alpha not equal q(-m), m is an element of N-0. Consequently, the present work is focused on the polynomials Bn,q(f; x) for the functions of the form f (x) = (x - q(-m))(-j) with j >= 2. For such functions, it is proved that the interval of convergence of {B-n,B-q(f; x)} depends not only on the location, but also on the multiplicity of the pole - a phenomenon which has not been considered previously. (C) 2013 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/openAccessq-Integerq-Bernstein polynomialConvergenceApproximation of unbounded functionsRational functionMultiple poleArticleQ2Q24132547556WOS:000331344600001