Turan, MehmetOstrovska, SofiyaTuran, MehmetOstrovska, SofiyaMathematics2024-07-052024-07-05202010035-75961945-379510.1216/rmj.2020.50.10852-s2.0-85091883204https://doi.org/10.1216/rmj.2020.50.1085https://hdl.handle.net/20.500.14411/3045For q is an element of (0, 1), let B-q denote the limit q-Bernstein operator. The distance between B-q and B-r for distinct q and r in the operator norm on C[0, 1] is estimated, and it is proved that 1 <= parallel to B-q - B-r parallel to <= 2, where both of the equalities can be attained. Furthermore, the distance depends on whether or not r and q are rational powers of each other. For example, if r(j) not equal q(m) for all j, m is an element of N, then parallel to B-q - B-r parallel to = 2, and if r = q(m) for some m is an element of N, then parallel to B-q - B-r parallel to = 2(m - 1)/m.eninfo:eu-repo/semantics/openAccesslimit q-Bernstein operatorPeano kernelpositive linear operatorsArticleQ350310851096WOS:000557770100021