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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: 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.
