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Article Citation - WoS: 47Citation - Scopus: 68On the Positive Solutions of the System of Rational Difference Equations(Academic Press inc Elsevier Science, 2006) Ozban, Ahmet YasarOur aim in this paper is to investigate the periodic nature of solutions of the system of rational difference equations x(n+1) = 1/y(n-k), y(n+1) = yn/x(n-mYn-m-k), n = 0, 1,..., where k is a nonnegative integer, m is a positive integer and the initial values x(-m), x(-m+1),..., x(0), y(-m-k), y(-m-k+1),..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.Article Polynomial Logistic Distribution Associated With a Cubic Polynomial(Taylor & Francis inc, 2017) Aksoy, Umit; Ostrovska, Sofiya; Ozban, Ahmet YasarLet P(x) be a polynomial monotone increasing on ( - , +). The probability distribution possessing the distribution function is called the polynomial logistic distribution with associated polynomial P. This has recently been introduced by Koutras etal., who have also demonstrated its importance for modeling financial data. In this article, the properties of the polynomial logistic distribution with an associated polynomial of degree 3 have been investigated in detail. An example of polynomial logistic distribution describing daily exchange rate fluctuations for the US dollar versus the Turkish lira is provided.Article On the Convergence of the q-bernstein Polynomials for Power Functions(Springer Basel Ag, 2021) Ostrovska, Sofiya; Ozban, Ahmet YasarThe aim of this paper is to present new results related to the convergence of the sequence of the complex q-Bernstein polynomials {B-n,B-q(f(alpha); z)}, where 0 < q not equal 1 and f(alpha) = x(alpha), alpha >= 0, is a power function on [0, 1]. This study makes it possible to describe all feasible sets of convergence K for such polynomials. Specifically, if either 0 < q < 1 or alpha is an element of N-0, then K = C, otherwise K = {0} boolean OR {q(-j)}(j=0)(infinity). In the latter case, this identifies the sequence K = {0} boolean OR {q(-j)}(j=0)(infinity) as the 'minimal' set of convergence for polynomials B-n,B-q(f; z), f is an element of C[0, 1] in the case q > 1. In addition, the asymptotic behavior of the polynomials {B-n,B-q(f(alpha); z)}, with q > 1 has been investigated and the obtained results are illustrated by numerical examples.Article Citation - WoS: 2Citation - Scopus: 2HOW DO SINGULARITIES OF FUNCTIONS AFFECT THE CONVERGENCE OF q-BERNSTEIN POLYNOMIALS?(Element, 2015) Ostrovska, Sofiya; Ozban, Ahmet Yasar; Turan, MehmetIn this article, the approximation of functions with a singularity at alpha is an element of (0, 1) by the q-Bernstein polynomials for q > 1 has been studied. Unlike the situation when alpha is an element of (0, 1) \ {q(-j)} j is an element of N, in the case when alpha = q(-m), m is an element of N, the type of singularity has a decisive effect on the set where a function can be approximated. In the latter event, depending on the types of singularities, three classes of functions have been examined, and it has been found that the possibility of approximation varies considerably for these classes.Article Uncorrelatedness Sets of Discrete Random Variables Via Vandermonde-Type Determinants(Walter de Gruyter Gmbh, 2019) Turan, Mehmet; Ostrovska, Sofiya; Ozban, Ahmet YasarGiven random variables X and Y having finite moments of all orders, their uncorrelatedness set is defined as the set of all pairs (j, k) is an element of N-2; for which X-j and Y-kappa are uncorrelated. It is known that, broadly put, any subset of N-2 can serve as an uncorrelatedness set. This claim is no longer valid for random variables with prescribed distributions, in which case the need arises so as to identify the possible uncorrelatedness sets. This paper studies the uncorrelatedness sets for positive random variables uniformly distributed on three points. Some general features of these sets are derived. Two related Vandermonde-type determinants are examined and applied to describe uncorrelatedness sets in some special cases. (C) 2019 Mathematical Institute Slovak Academy of SciencesArticle Citation - WoS: 6Citation - Scopus: 7On the q-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.
