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On the Eigenstructure of the Modified Bernstein Operators
(Taylor & Francis inc, 2022) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, Mehmet
Starting from the well-known work of Cooper and Waldron published in 2000, the eigenstructure of various Bernstein-type operators has been investigated by many researchers. In this work, the eigenvalues and eigenvectors of the modified Bernstein operators Q(n) have been studied. These operators were introduced by S. N. Bernstein himself, in 1932, for the purpose of accelerating the approximation rate for smooth functions. Here, the explicit formulae for the eigenvalues and corresponding eigenpolynomials together with their limiting behavior are established. The results show that although some outcomes are similar to those for the Bernstein operators, there are essentially different ones as well.
Citation - WoS: 3
Citation - Scopus: 3
On the Metric Space of the Limit q-bernstein Operators
(Taylor & Francis inc, 2019) Ostrovska, Sofiya; Turan, Mehmet
In 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.