Ostrovska, Sofiya
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Ostrovska, Sofıya & Ostrovska,S. & Ostrovska, Sofia & S., Ostrovska & S.,Ostrovska & O., Sofiya & Ostrovska, S & Sofiya, Ostrovska & Ostrovska, S. & Ostrovska, Sofiya & Ostrovska S. & O.,Sofiya
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sofia.ostrovska@atilim.edu.tr
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Mathematics
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2ZERO HUNGER
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Documents
102
Citations
939
h-index
14
Documents
89
Citations
833
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Scholarly Output
112
Articles
104
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123/129
Supervised MSc Theses
3
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WoS Citation Count
845
Scopus Citation Count
949
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0
WoS Citations per Publication
7.54
Scopus Citations per Publication
8.47
Open Access Source
45
Supervised Theses
3
| Journal | Count |
|---|---|
| Journal of Mathematical Analysis and Applications | 8 |
| Mediterranean Journal of Mathematics | 4 |
| Results in Mathematics | 4 |
| Journal of Approximation Theory | 4 |
| Statistics & Probability Letters | 4 |
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112 results
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Now showing 1 - 10 of 112
Article Citation - WoS: 1Citation - Scopus: 1The Convergence of <i>q</I>-bernstein Polynomials (0 < <i>q</I> < 1) and Limit <i>q</I>-bernstein Operators in Complex Domains(Rocky Mt Math Consortium, 2009) Ostrovska, Sofiya; Wang, HepingDue to the fact that the convergence properties of q-Bernstein polynomials are not similar to those in the classical case q = 1, their study has become an area of intensive research with a wide scope of open problems and unexpected results. The present paper is focused on the convergence of q-Bernstein polynomials, 0 < q < 1, and related linear operators in complex domains. An analogue of the classical result on the simultaneous approximation is presented. The approximation of analytic functions With the help of the limit q-Bernstein operator is studied.Article Dvoretzky-Type Theorem for Locally Finite Subsets of a Hilbert Space(Annales Inst Fourier, 2025) Catrina, Florin; Ostrovska, Sofiya; Ostrovskii, Mikhail I.The main result of the paper: Given any epsilon > 0, every locally finite subset of l(2) admits a (1 + epsilon)-bilipschitz embedding into an arbitrary infinite-dimensional Banach space. The result is based on two results which are of independent interest: (1) A direct sum of two finite-dimensional Euclidean spaces contains a sub-sum of a controlled dimension which is epsilon-close to a direct sum with respect to a 1-unconditional basis in a two-dimensional space. (2) For any finite-dimensional Banach space Y and its direct sum X with itself with respect to a 1-unconditional basis in a two-dimensional space, there exists a (1 + epsilon)-bilipschitz embedding of Y into X which on a small ball coincides with the identity map onto the first summand and on the complement of a large ball coincides with the identity map onto the second summand.Article Citation - WoS: 2Citation - Scopus: 2On the eigenfunctions of the <i>q</i>-Bernstein operators(Springer Basel Ag, 2023) Ostrovska, Sofiya; Turan, MehmetThe eigenvalue problems for linear operators emerge in various practical applications in physics and engineering. This paper deals with the eigenvalue problems for the q-Bernstein operators, which play an important role in the q-boson theory of modern theoretical physics. The eigenstructure of the classical Bernstein operators was investigated in detail by S. Cooper and S. Waldron back in 2000. Some of their results were extended for other Bernstein-type operators, including the q-Bernstein and the limit q-Bernstein operators. The current study is a pursuit of this research. The aim of the present work is twofold. First, to derive for the q-Bernstein polynomials analogues of the Cooper-Waldron results on zeroes of the eigenfunctions. Next, to present in detail the proof concerning the existence of non-polynomial eigenfunctions for the limit q-Bernstein operator.Article On the Injectivity With Respect To <i>q</I> of the Lupas <i>q</I>-transform(Taylor & Francis Ltd, 2024) Yilmaz, Ovgue Gurel; Ostrovska, Sofiya; Turan, Mehmet; Gurel Yilmaz, OvguThe Lupas q-transform has first appeared in the study of the Lupas q-analogue of the Bernstein operator. Given 0 < q < 1 and f is an element of C[0, 1], the Lupas q-transform is defined by Lambda(q)(f; x) Pi(infinity)(k=0) 1/1 + q(k)x Sigma(k=0)f(1 - q(k))q(k(k-1)/2)x(k)/(1 - q)(1 - q(2)) center dot center dot center dot (1 - q(k)), x >= 0. During the last decades, this transform has been investigated from a variety of angles, including its analytical, geometric features, and properties of its block functions along with their sums. As opposed to the available studies dealing with a fixed value of q, the present work is focused on the injectivity of Lambda(q) with respect to parameter q. More precisely, the conditions on f such that equality Lambda(q)(f; x) = Lambda(r)(f; x); x >= 0 implies q = r have been established.Article On the Lupas <i>q</I>-transform of Unbounded Functions(Walter de Gruyter Gmbh, 2023) Ostrovska, Sofiya; Turan, MehmetThe Lupa , s q-transform comes out naturally in the study of the Lupa , s q-analogue of the Bernstein operator. It is closely related to the Heine q-distribution which has a numerous application in q-boson operator calculus and to the Valiron method of summation for divergent series. In this paper, the Lupa , s q-transform (lambda(q)f)(z), q is an element of (0, 1), of unbounded functions is considered in distinction to the previous researches, where only the case f is an element of C[0, 1] have been investigated. First, the condition for a function to possess the Lupa , s q-transform is presented. Also, results concerning the connection between growth rate of the function f (t) as t -> 1(-) and the growth of its Lupa , s q-transform (lambda(q)f)(z) as z -> infinity are established. (c) 2023 Mathematical Institute Slovak Academy of SciencesMaster Thesis Q-bernstein Polinomlarının Özellikleri Üzerine(2017) Almesbahı, Manal Mastafa; Turan, Mehmet; Ostrovska, SofıyaBu tezin amacı Bernstein polinomları teorisini ve son genişletmesi olan q-kalkülüsü çalışmaktır. Bu çalışmanın temel odak noktası 20 yıl önce ortaya çıkan ve kısa sürede birçok araştırmacının dikkatini çeken q-Bernstein polinomlarıdır. Bu tez Bernstein polinomlarına dair bilinen bazı sonuçların derlemesinden, q-Bernstein polinomları teorisine kısa bir giriş ve bazı yeni gelişmelerden oluşmaktadır. Yeni gelişmeler kısmında; limit q-Bernstein operatör dizisinin kuvvetli operatör limiti ve q-Bernstein operatörlerinin zayıf Picard operatörler oldukları ifade edilmiştir.Master Thesis Limit Q-Bernstein Tipi Operatörlerin Birleştirilmesine Yönelik Bir Yaklaşım(2025) Pirimoğlu, Lütfi Atahan; Turan, Mehmet; Ostrovska, SofıyaBu tez, yeni oluşturulan ve birleştirici operatör olarak adlandırılan U operatörünün yardımıyla limit q-Bernstein türü operatörlerin bir çarpanlara ayrımını sunmayı amaçlamaktadır. Bu operatör, bilinen operatörlerin iki daha basit bileşenin çarpımı olarak ayrıştırılmasında evrensel bir sol çarpan olarak görev yapmaktadır. Tezin ilk bölümünde, U operatörünün çeşitli özellikleri ortaya konmaktadır. Daha sonra, önceden bilinen limit q-Bernstein türü operatörlere uygulamalar gösterilmektedir. Bu çarpanlara ayırma yöntemiyle bazı yeni sonuçlar elde edilmiştir. Tezin kalan kısmı yeni bir limit operatörün bulunmasına ve özelliklerinin incelenmesine ayrılmıştır.Article Citation - WoS: 6Citation - Scopus: 7On the <i>q</I>-bernstein Polynomials of Rational Functions With Real Poles(Academic Press inc Elsevier Science, 2014) Ostrovska, Sofiya; Ozban, Ahmet YasarThe paper aims to investigate the convergence of the q-Bernstein polynomials B-n,B-q(f; x) attached to rational functions in the case q > 1. The problem reduces to that for the partial fractions (x - alpha)(-J), j is an element of N. The already available results deal with cases, where either the pole a is simple or alpha not equal q(-m), m is an element of N-0. Consequently, the present work is focused on the polynomials Bn,q(f; x) for the functions of the form f (x) = (x - q(-m))(-j) with j >= 2. For such functions, it is proved that the interval of convergence of {B-n,B-q(f; x)} depends not only on the location, but also on the multiplicity of the pole - a phenomenon which has not been considered previously. (C) 2013 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3On the Metric Space of the Limit <i>q</I>-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 Citation - WoS: 1Citation - Scopus: 2The Functional-Analytic Properties of the Limit <i>q</I>-bernstein Operator(Hindawi Ltd, 2012) Ostrovska, SofiyaThe limit q-Bernstein operator B-q, 0 < q < 1, emerges naturally as a modification 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. Lately, the limit q-Bernstein operator has been widely under scrutiny, and it has been shown that B-q is a positive shape-preserving linear operator on C[0, 1] with parallel to B-q parallel to = 1. Its approximation properties, probabilistic interpretation, eigenstructure, and impact on the smoothness of a function have been examined. In this paper, the functional-analytic properties of B-q are studied. Our main result states that there exists an infinite-dimensional subspace M of C[0, 1] such that the restriction B-q vertical bar(M) is an isomorphic embedding. Also we show that each such subspace M contains an isomorphic copy of the Banach space c(0).