Turan, Mehmet

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https://hdl.handle.net/20.500.14411/6771
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T., Mehmet
Turan M.
M.,Turan
Turan,Mehmet
Mehmet, Turan
T.,Mehmet
Turan A.
Mehmet Turan
M., Turan
Turan, Mehmet
Turan,M.
Turan, M.
Job Title
Profesör Doktor
Email Address
mehmet.turan@atilim.edu.tr
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Mathematics
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Scholarly Output

55

Articles

44

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241/2899

Supervised MSc Theses

5

Supervised PhD Theses

2

WoS Citation Count

82

Scopus Citation Count

95

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WoS Citations per Publication

1.49

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1.73

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Mathematical Methods in the Applied Sciences3
Numerical Functional Analysis and Optimization2
Quaestiones Mathematicae2
Results in Mathematics2
Mathematica Slovaca2
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Scholarly Output Search Results

Now showing 1 - 10 of 39
  • Thumbnail Image
    Article
    How Analytic Properties of Functions Influence Their Images Under the Limit q-Stancu Operator
    (Springer Basel AG, 2026) Gurel, Ovgu; Ostrovska, Sofiya; Turan, Mehmet
    In 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.
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    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, Mehmet
    The 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.
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    Article
    On the Image of the Limit Q-Durrmeyer Operator
    (Academic Press Inc Elsevier Science, 2026) Ostrovska, Sofiya; Turan, Mehmet
    The 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.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 1
    The Truncated q-bernstein Polynomials in the Case q > 1
    (Hindawi Ltd, 2014) Turan, Mehmet
    The truncated q-Bernstein polynomials B-n,B-m,B-q (f; x), n is an element of N, and m is an element of N-0 emerge naturally when the q-Bernstein polynomials of functions vanishing in some neighbourhood of 0 are considered. In this paper, the convergence of the truncated q-polynomials on [0, 1] is studied. To support the theoretical results, some numerical examples are provided.
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    Conference Object
    Citation - WoS: 2
    The Limit q-bernstein Operators With Varying q
    (Springer international Publishing Ag, 2019) Almesbahi, Manal Mastafa; Ostrovska, Sofiya; Turan, Mehmet
    [No Abstract Available]
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    Conference Object
    Density-Aware Outage in Clustered Ad Hoc Networks
    (Ieee, 2018) Eroglu, Alperen; Onur, Ertan; Turan, Mehmet
    Density 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.
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    Article
    Fedja’s Proof of Deepti’s Inequality
    (Tubitak Scientific & Technological Research Council Turkey, 2018) Ostrovska, Sofiya; Turan, Mehmet
    The 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.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 1
    On the q-moment Determinacy of Probability Distributions
    (Malaysian Mathematical Sciences Soc, 2020) Ostrovska, Sofiya; Turan, Mehmet
    Given 0
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    Article
    Citation - WoS: 4
    Citation - Scopus: 4
    On the Powers of the Kummer Distribution
    (Academic Publication Council, 2017) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
    The Kummer distribution is a probability distribution, whose density is given by f (x) = cx (alpha-1)(1 + delta x)(-gamma) e(-beta x), X > 0, where alpha, beta, delta > 0, gamma is an element of R and C is a normalizing constant. In this paper, the distributions of random variable X-P, p > 0, where X has the Kummer distribution, are considered with the conditions being IFR/DFR, some properties of moments depending on the parameters and the moment-(in) determinacy. In the case of moment-indeterminacy, exemplary Stieltjes classes are constructed.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 1
    The Distance Between Two Limit q-bernstein Operators
    (Rocky Mt Math Consortium, 2020) Ostrovska, Sofiya; Turan, Mehmet
    For q is an element of (0, 1), let B-q denote the limit q-Bernstein operator. The distance between B-q and B-r for distinct q and r in the operator norm on C[0, 1] is estimated, and it is proved that 1 <= parallel to B-q - B-r parallel to <= 2, where both of the equalities can be attained. Furthermore, the distance depends on whether or not r and q are rational powers of each other. For example, if r(j) not equal q(m) for all j, m is an element of N, then parallel to B-q - B-r parallel to = 2, and if r = q(m) for some m is an element of N, then parallel to B-q - B-r parallel to = 2(m - 1)/m.