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Article On the Lupas q-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 SciencesArticle On the Image of the Limit Q-Durrmeyer Operator(Academic Press Inc Elsevier Science, 2026) Ostrovska, Sofiya; Turan, MehmetThe focus of this work is on the properties of the q-Durrmeyer operators Mn,q, n E N, and M infinity,q introduced, for q E (0, 1), by V. Gupta and H. Wang. First, it is shown that, for each f E C[0, 1], the sequence {Mn,q f}nEN converges to M infinity,q f uniformly on [0, 1] with a rate not slower than Cq, fqn, which refines the previously available result by V. Gupta and H. Wang, and implies the possibility of an analytic continuation for M infinity,q f into a neighbourhood of [0, 1]. Further investigation shows that M infinity,q f admits an analytic continuation as an entire function regardless of f E C[0, 1]. Finally, the growth estimates for these functions are received and applied to describe the point spectrum of M infinity,q. The paper also addresses the significant differences between the properties of M infinity,q and the previously (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.Article Citation - WoS: 1Citation - Scopus: 1On the q-moment Determinacy of Probability Distributions(Malaysian Mathematical Sciences Soc, 2020) Ostrovska, Sofiya; Turan, MehmetGiven 0Conference Object Citation - WoS: 2The Limit q-bernstein Operators With Varying q(Springer international Publishing Ag, 2019) Almesbahi, Manal Mastafa; Ostrovska, Sofiya; Turan, Mehmet[No Abstract Available]Conference Object Density-Aware Outage in Clustered Ad Hoc Networks(Ieee, 2018) Eroglu, Alperen; Onur, Ertan; Turan, MehmetDensity of ad hoc networks may vary in time and space because of mobile stations, sleep scheduling or failure of nodes. Resources such as spectrum will be wasted if the network is not density-aware and -adaptive. Towards this aim, distributed and robust network density estimators are required. In this paper, we propose a novel cluster density estimator in random ad hoc networks by employing distance matrix. Monte-Carlo simulation results validate the proposed estimator. The accuracy of the estimator is impressive even under a high amount of distance measurement errors. We also propose a network outage model and a transmit power adaption technique that are density-aware. The results indicate the necessity of the density-aware solutions for making network performance better from capacity, coverage and energy conservation viewpoints.Master 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.Article Fedja’s Proof of Deepti’s Inequality(Tubitak Scientific & Technological Research Council Turkey, 2018) Ostrovska, Sofiya; Turan, MehmetThe paper aims to present, in a systematic way, an elegant proof of Deepti’s inequality. Both the inequalityand various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none haveappeared in the literature thus far. In this work, suggestions pertaining to users ‘Deepti’ and ‘fedja’ are traced, whencethe title. The results or the paper are new, and the proof is divided into a series of statements, many of which are ofinterest in themselves.Article How Analytic Properties of Functions Influence Their Images Under the Limit q-Stancu Operator(Springer Basel AG, 2026) Gurel, Ovgu; Ostrovska, Sofiya; Turan, MehmetIn the study of various q-versions of the Bernstein polynomials, a significant attention is paid to their limit operators. The present work focuses on the impact of the limit q-Stancu operator Sq infinity,alpha on the analytic properties of functions when 0 < q < 1 and alpha > 0. It is shown that for every f is an element of C[0, 1], the function S-q,(alpha infinity)fadmits an analytic continuation into the disk {z : z+alpha/(1-q) < 1+ alpha/(1-q)}. In addition, it is proved that the more derivatives f has at x = 1, the wider this disk becomes. Further, if f is infinitely differentiable at x = 1, then the function S-q,(alpha infinity)fis entire. Finally, some growth estimates for (S-q,(alpha infinity)f)(z) are obtained.Article Citation - WoS: 2Citation - Scopus: 1The Continuity in Q of the Lupaş Q-Analogues of the Bernstein Operators(Academic Press inc Elsevier Science, 2024) Yilmaz, Ovgue Gurel; Turan, Mehmet; Ostrovska, Sofiya; Turan, Mehmet; Ostrovska, Sofiya; Turan, Mehmet; Ostrovska, Sofiya; Mathematics; MathematicsThe Lupas q-analogue Rn,q of the Bernstein operator is the first known q-version of the Bernstein polynomials. It had been proposed by A. Lupas in 1987, but gained the popularity only 20 years later, when q-analogues of classical operators pertinent to the approximation theory became an area of intensive research. In this work, the continuity of operators Rn,q with respect to parameter q in the strong operator topology and in the uniform operator topology has been investigated. The cases when n is fixed and n -> infinity have been considered. (c) 2022 Elsevier Inc. All rights reserved.Article On the Moment-Determinacy of Power Lindley Distribution and Some Applications To Software Metrics(Acad Brasileira de Ciencias, 2021) Khalleefah, Mohammed; Ostrovska, Sofiya; Turan, MehmetThe Lindley distribution and its numerous generalizations are widely used in statistical and engineering practice. Recently, a power transformation of Lindley distribution, called the power Lindley distribution, has been introduced by M. E. Ghitany et at who initiated the investigation of its properties and possible applications. In this article, new results on the power Lindley distribution are presented. The focus of this work is on the moment-(in)determinacy of the distribution for various values of the parameters. Afterwards, certain applications are provided to describe data sets of software metrics.
