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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 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.
