Ostrovska, SofiyaOzban, Ahmet YasarMathematics2024-07-052024-07-05201160898-12211873-766810.1016/j.camwa.2011.10.0672-s2.0-82255160739https://doi.org/10.1016/j.camwa.2011.10.067https://hdl.handle.net/20.500.14411/1284The aim of this paper is to present norm estimates in C [0, 1] for the q-Bernstein basic polynomials and the q-Bernstein operators B-n,B-q in the case q > 1. While for 0 < q <= 1, vertical bar vertical bar B-n,B-q vertical bar vertical bar = 1 for all n is an element of N. in the case q > 1, the norm vertical bar vertical bar B-n,B-q vertical bar vertical bar increases rather rapidly as q -> +infinity. In this study, it is proved that vertical bar vertical bar B-n,B-q vertical bar vertical bar similar to C(n)q(n(n-1)/2), q -> +infinity with C-n = 2/n (1- 1/n)(n-1). Moreover, it is shown that vertical bar vertical bar B-n,B-q vertical bar vertical bar similar to 2q(n(n-1)/2) /ne as n -> infinity, q -> +infinity. The results of the paper are illustrated by numerical examples. (C) 2011 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/closedAccessq-integersq-binomial coefficientsq-Bernstein polynomialsq-Bernstein operatorOperator normNewton's methodArticleQ1621247584771WOS:000298824900047