Ostrovska, SofiyaMathematics2024-07-052024-07-0520121029-242X10.1186/1029-242X-2012-2972-s2.0-84876592357https://doi.org/10.1186/1029-242X-2012-297https://hdl.handle.net/20.500.14411/1406The limit q-Bernstein operator B-q emerges naturally as a modification of the Szasz-Mirakyan operator related to the Euler probability distribution. At the same time, this operator serves as the limit for a sequence of the q-Bernstein polynomials with 0 < q < 1. Over the past years, the limit q-Bernstein operator has been studied widely from different perspectives. Its approximation, spectral, and functional-analytic properties, probabilistic interpretation, the behavior of iterates, and the impact on the analytic characteristics of functions have been examined. It has been proved that under a certain regularity condition, B-q improves the smoothness of a function which does not satisfy the Holder condition. The purpose of this paper is to exhibit 'exceptional' functions whose smoothness is not improved under the limit q-Bernstein operator. MSC: 26A15; 26A16; 41A36eninfo:eu-repo/semantics/openAccesslimit q-Bernstein operatorHolder conditionmodulus of continuityArticleQ1WOS:0003178468000061