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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 Citation - WoS: 45Citation - Scopus: 61On the System of Rational Difference Equations xn = a yn< = byn-3<(Elsevier Science inc, 2007) Ozban, Ahmet YasarIn this paper we investigate the behaviour of the positive solutions of the system of rational difference equation x(n) = a/y(n-3), y(n) = by(n-3)/x(n-q)Y(n-q), n = 1, 2,..., where q > 3 is a positive integer with 3 inverted iota q, a and b are positive constants and tile initial values x(-q+1),x(-q+2),...,x0, Y-q+1,y(-q+2),...,y(0) are positive real numbers. (C) 2006 Elsevier Inc. All rights reserved.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: 3Citation - Scopus: 4New Methods for Approximating Square Roots(Elsevier Science inc, 2006) Ozban, Ahmet YasarSome new higher order iterative methods are obtained to approximate the positive square root of a positive real number. Moreover some numerical tests are performed to demonstrate the performances and accuracies of the new methods. The numerical results show that the methods we obtain are competitive with the existing ones. (c) 2005 Published by Elsevier Inc.Article Citation - WoS: 3Citation - Scopus: 3The q-bernstein Polynomials of the Cauchy Kernel With a Pole on [0,1] in the Case q > 1(Elsevier Science inc, 2013) Ostrovska, Sofiya; Ozban, Ahmet YasarThe problem to describe the Bernstein polynomials of unbounded functions goes back to Lorentz. The aim of this paper is to investigate the convergence properties of the q-Bernstein polynomials B-n,B-q(f; x) of the Cauchy kernel 1/x-alpha with a pole alpha is an element of [0, 1] for q > 1. The previously obtained results allow one to describe these properties when a pole is different from q(-m) for some m is an element of {0, 1, 2, ...}. In this context, the focus of the paper is on the behavior of polynomials B-n,B-q(f; x) for the functions of the form f(m)(x) = 1/(x - q(-m)), x not equal q(-m) and f(m)(q(-m)) = a, a is an element of R. Here, the problem is examined both theoretically and numerically in detail. (C) 2013 Elsevier Inc. All rights reserved.Article Citation - WoS: 22Citation - Scopus: 21On idempotency and tripotency of linear combinations of two commuting tripotent matrices(Elsevier Science inc, 2009) Ozdemir, Halim; Sarduvan, Murat; Ozban, Ahmet Yasar; Guler, NesrinLet T-1 and T-2 be two nonzero commuting n x n tripotent matrices and c(1), c(2) two nonzero complex numbers. Necessary and sufficient conditions for the tripotency and the idempotency of c(1)T(1) + c(2)T(2) are obtained. The problems considered here have also statistical importance when c(1), c(2) are real scalars and T-1, T-2 are real symmetric matrices. (C) 2008 Elsevier Inc. All rights reserved.Article 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.Article Citation - WoS: 5Citation - Scopus: 6The Norm Estimates of the q-bernstein Operators for Varying q > 1(Pergamon-elsevier Science Ltd, 2011) Ostrovska, Sofiya; Ozban, Ahmet YasarThe aim of this paper is to present norm estimates in C [0, 1] for the q-Bernstein basic polynomials and the q-Bernstein operators B-n,B-q in the case q > 1. While for 0 < q <= 1, vertical bar vertical bar B-n,B-q vertical bar vertical bar = 1 for all n is an element of N. in the case q > 1, the norm vertical bar vertical bar B-n,B-q vertical bar vertical bar increases rather rapidly as q -> +infinity. In this study, it is proved that vertical bar vertical bar B-n,B-q vertical bar vertical bar similar to C(n)q(n(n-1)/2), q -> +infinity with C-n = 2/n (1- 1/n)(n-1). Moreover, it is shown that vertical bar vertical bar B-n,B-q vertical bar vertical bar similar to 2q(n(n-1)/2) /ne as n -> infinity, q -> +infinity. The results of the paper are illustrated by numerical examples. (C) 2011 Elsevier Ltd. All rights reserved.
