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Article Citation - WoS: 7On the Approximation of Analytic Functions by the q-bernstein Polynomials in the Case q > 1(Kent State University, 2010) Ostrovska, SofiyaSince for q > 1, the q-Bernstein polynomials B(n,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 is an element of C[0, 1] and admits an analytic continuation f(z) into {z : |z| < a}, then B(n,q) (f; z) -> f (z) as n -> infinity, uniformly on any compact set in {z : |z| < a}.Article Citation - WoS: 12Citation - Scopus: 13Assessing Team Work in Engineering Projects(Tempus Publications, 2015) Mishra, Deepti; Ostrovska, Sofiya; Hacaloglu, Tuna; Mathematics; Computer Engineering; Information Systems EngineeringTeam work is considered a valuable teaching technique in higher education. However, the assessment of an individual's work in teams has proved to be a challenging task. Consequently, self-and peer-evaluations are becoming increasingly popular for the assessment of individuals in a team work, though it is essential to determine whether students can judge their own as well as their peer's performance effectively. Self-and peer-evaluations have been applied in different disciplines and their authenticity with regard to teacher's assessment has been evaluated in the literature but this issue has not been investigated in the field of engineering education so far. In this study, a peer-and self-assessment procedure is applied to the evaluation of a project work conducted in teams of 3 or 4 students. The participants were engineering students taking two similar courses related with database design and development. It is found that a majority of the students were unable to assess themselves as objectively as their instructor. Further, it is observed that successful students tend to under-estimate, whereas unsuccessful students tend to over-estimate, their own performance. The paper also establishes that the results of self-assessments are independent from the gender factor.Article A Decomposition of the Limit Q-Bernstein Type Operators Via a Universal Factor(Springer Basel AG, 2026) Ostrovska, Sofiya; Pirimoglu, Lutfi Atahan; Turan, MehmetThe focus of this work is on the properties of the unifying operator Uq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_q$$\end{document} on C[0, 1], which serves as a universal left factor in a decomposition of the limit q-Bernstein type operators, L infinity,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\infty ,q}$$\end{document}. More precisely, the factorization L infinity,q=Uq degrees TL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\infty ,q}= U_q\circ T_L$$\end{document}, where TL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_L$$\end{document} is a linear operator on C[0, 1] depending on L, holds. It is shown that this factorization facilitates the derivation of new results and/or the simplification of proofs for the known ones.Article Citation - WoS: 2The Approximation of Power Function by the q-bernstein Polynomials in the Case q > 1(Element, 2008) Ostrovska, SofiyaSince 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)(alpha), a >= 0. with a non-integer alpha > -1 is studied. It is proved that for a > 0, the function is uniformly approximated on any compact set in {z : vertical bar z vertical bar < a}, while on any Jordan arc in {z : vertical bar z vertical bar > a}. the uniform approximation is impossible, In the case a = 0(1) the results of the paper reveal the following interesting phenomenon: the power function z(alpha), alpha > 0: is approximated by its, q-Bernstein polynomials either on any (when alpha is an element of N) or no (when alpha is not an element of N) Jordan arc in C.Article Citation - WoS: 1Distortion in the Metric Characterization of Superreflexivity in Terms of the Infinite Binary Tree(Element, 2022) Ostrovska, SofiyaThe article presents a quantitative refinement of the result of Baudier (Archiv Math., 89 (2007), no. 5, 419-429): the infinite binary tree admits a bilipschitz embedding into an arbitrary non-superreflexive Banach space. According to the results of this paper, we can additionally require that, for an arbitrary epsilon > 0 and an arbitrary non-superreflexive Banach space X, there is an embedding of the infinite binary tree into X whose distortion does not exceed 4 + epsilon .Article Citation - WoS: 11Citation - Scopus: 15The q-versions of the Bernstein Operator: From Mere Analogies To Further Developments(Springer Basel Ag, 2016) Ostrovska, SofiyaThe article exhibits a review of results on two popular q-versions of the Bernstein polynomials, namely, the LupaAY q-analogue and the q-Bernstein polynomials. Their similarities and distinctions are discussed.Article On the Eigenstructure of the Modified Bernstein Operators(Taylor & Francis inc, 2022) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, MehmetStarting 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.Article Citation - WoS: 2Citation - Scopus: 2Distortion of Embeddings of Binary Trees Into Diamond Graphs(Amer Mathematical Soc, 2018) Leung, Siu Lam; Nelson, Sarah; Ostrovska, Sofiya; Ostrovskii, MikhailDiamond graphs and binary trees are important examples in the theory of metric embeddings and also in the theory of metric characterizations of Banach spaces. Some results for these families of graphs are parallel to each other; for example superreflexivity of Banach spaces can be characterized both in terms of binary trees (Bourgain, 1986) and diamond graphs (Johnson-Schechtman, 2009). In this connection, it is natural to ask whether one of these families admits uniformly bilipschitz embeddings into the other. This question was answered in the negative by Ostrovskii (2014), who left it open to determine the order of growth of the distortions. The main purpose of this paper is to get a sharp up-to-a-logarithmic-factor estimate for the distortions of embeddings of binary trees into diamond graphs and, more generally, into diamond graphs of any finite branching k >= 2. Estimates for distortions of embeddings of diamonds into infinitely branching diamonds are also obtained.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.Article On Quasi-Weibull Distribution(Univ Miskolc inst Math, 2025) Ostrovska, Sofiya; Turan, MehmetExponential distribution together with a variety of its transformations is permanently used both in probability theory and related fields. The most popular one is the power transformation yielding the Weibull distribution. In this paper, the power distribution of exponential random variable is supplemented by a logarithmic factor leading to a new distribution called quasi-Weibull. This is a three-parameter distribution, where one parameter is inherited from the underlying exponential distribution, and the others originate from the transformation. The properties of the quasi-Weibull distribution are studied. Specifically, the impact of the parameters on the analyticity of characteristic function, the existence of the moment generating function, the moment-determinacy/indeterminacy and the behaviour of the hazard function are investigated.
