Kaskaloglu, KeremOstrovska, SofiyaMathematics2024-07-052024-07-0520130895-71771872-947910.1016/j.mcm.2012.01.0222-s2.0-84875679564https://doi.org/10.1016/j.mcm.2012.01.022https://hdl.handle.net/20.500.14411/444The aim of this paper is to present new results related to the approximation of continuous functions by their q-Bernstein polynomials in the case q > 1. The first part of the paper is devoted to the behavior of the q-Bernstein polynomials of piecewise linear functions. This study naturally leads to the notion of truncated q-Bernstein polynomials introduced in the paper. The second part deals with the asymptotic estimates for the norms of the m-truncated q-Bernstein polynomials, in the case where both n and q vary. The results of the paper are illustrated by numerical examples. (C) 2012 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/openAccessq-integersq-binomial coefficientsq-Bernstein polynomialsq-Bernstein operatorOperator normArticle579-1024192431WOS:0003172621000413