Browsing by Author "Ostrovska,S."

Now showing 1 - 6 of 6

Citation - Scopus: 2
The Approximation of Power Function by the Q-Bernstein Polynomials in the Case Q > 1
(Element D.O.O., 2008) Ostrovska,S.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Since for q > 1, q-Bernstein polynomials are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. It is known that, in the case q > 1, the q-Bernstein polynomials approximate the entire functions and, in particular, polynomials uniformly on any compact set in ℂ. In this paper, the possibility of the approximation for the function (z + a)α, a ≥ 0, with a non-integer α > -1 is studied. It is proved that for a > 0, the function is uniformly approximated on any compact set in {z: \z| < a}, while on any Jordan arc in {z: \z\ > a}, the uniform approximation is impossible. In the case a = 0, the results of the paper reveal the following interesting phenomenon: the power function zα, α > 0, is approximated by its q-Bernstein polynomials either on any (when α ∈ ℕ) or no (when α ∉ ℕ) Jordan arc in ℂ.
Citation - Scopus: 1
Approximation Theory and Numerical Analysis
(Hindawi Publishing Corporation, 2014) Ostrovska,S.; Berdysheva,E.; Nowak,G.; Özban,A.Y.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
[No abstract available]
Non-Asymptotic Norm Estimates for the Q-Bernstein Operators
(Springer New York LLC, 2013) Ostrovska,S.; Özban,A.Y.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The aim of this paper is to present new non-asymptotic norm estimates in C[0,1] for the q-Bernstein operators Bn,q in the case q > 1. While for 0 < q ≤ 1, {double pipe}Bn,q{double pipe} = 1 for all n ∈ ℕ, in the case q > 1, the norm {double pipe}Bn,q{double pipe} grows rather rapidly as n → + ∞ and q → + ∞. Both theoretical and numerical comparisons of the new estimates with the previously available ones are carried out. The conditions are determined under which the new estimates are better than the known ones. © Springer Science+Business Media New York 2013.
Citation - Scopus: 1
On Lin’s Condition for Products of Random Variables
(B. I. Verkin Institute for Low Temperature Physics and Engineering, 2019) Il’inskii,A.; Ostrovska,S.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The paper presents an elaboration of some results on Lin’s conditions. A new proof is given to the fact that if densities of independent random variables ξ 1 and ξ 2 satisfy Lin’s condition, then the same is true for their product. Also, it is shown that without the condition of independence, the statement is no longer valid. © Alexander Il’inskii and Sofiya Ostrovska, 2019.
Citation - Scopus: 7
On the Approximation of Analytic Functions by the Q-Bernstein Polynomials in the Case Q > 1
(Kent State University, 2010) Ostrovska,S.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Since for q > 1, the q-Bernstein polynomials Bn,q are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. In this paper, new results on the approximation of continuous functions by the q-Bernstein polynomials in the case q > 1 are presented. It is shown that if f Ε C[0, 1] and admits an analytic continuation f(z) into {z : |z| < a}, then Bn,q (f; z) → f(z) as n → λ, uniformly on any compact set in {z : |z| < a}. Copyright © 2010, Kent State University.
Qualitative Results on the Convergence of the Q-Bernstein Polynomials
(North University of Baia Mare, 2015) Ostrovska,S.; Turan,M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Despite many common features, the convergence properties of the Bernstein and the q-Bernstein polynomials are not alike. What is more, the cases 0 < q < 1 and q > 1 are not similar to each other in terms of convergence. In this work, new results demonstrating the striking differences which may occur in those convergence properties are presented. © 2015, North University of Baia Mare. All rights reserved.