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Article Citation - WoS: 1Citation - Scopus: 1The Distance Between Two Limit q-bernstein Operators(Rocky Mt Math Consortium, 2020) Ostrovska, Sofiya; Turan, MehmetFor 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.Article Citation - WoS: 3Citation - Scopus: 4The Unicity Theorems for the Limit Q-Bernstein Operator(Taylor & Francis Ltd, 2009) Ostrovska, SofiyaThe limit q-Bernstein operator [image omitted] emerges naturally as a q-version of the Szasz-Mirakyan operator related to the Euler distribution. The latter is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state. The limit q-Bernstein operator has been widely studied lately. It has been shown that [image omitted] is a positive shape-preserving linear operator on [image omitted] with [image omitted] Its approximation properties, probabilistic interpretation, the behaviour of iterates, eigenstructure and the impact on the smoothness of a function have been examined. In this article, we prove the following unicity theorem for operator: if f is analytic on [0, 1] and [image omitted] for [image omitted] then f is a linear function. The result is sharp in the following sense: for any proper closed subset [image omitted] of [0, 1] satisfying [image omitted] there exists a non-linear infinitely differentiable function f so that [image omitted] for all [image omitted].Article Citation - WoS: 3Citation - Scopus: 3On the Metric Space of the Limit q-bernstein Operators(Taylor & Francis inc, 2019) Ostrovska, Sofiya; Turan, MehmetIn this paper, some properties of uniformly discrete metric space are established. The metric rho comes out naturally in the evaluation of the distance between two limit q-Bernstein operators with respect to the operator norm on The exact value of this distance is found for all Furthermore, a number of properties of metric bases in M are presented alongside all possible isometries on M.
