The norm estimates of the qq-Bernstein operators for varying q>1q>1

The aim of this paper is to present norm estimates in C[0,1]C[0,1] for the qq-Bernstein basic polynomials and the qq-Bernstein operators Bn,qBn,q in the case q>1q>1. While for 01q>1, the norm ‖Bn,q‖‖Bn,q‖ increases rather rapidly as q→+∞q→+∞. In this study, it is proved that ‖Bn,q‖∼Cnqn(n−1)/2,q→+∞withCn=2n(1−1n)n−1. Moreover, it is shown that ‖Bn,q‖∼2qn(n−1)/2ne as n→∞,q→+∞. The results of the paper are illustrated by numerical examples.