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Citation - WoS: 1
Citation - Scopus: 1
On the Invariant Manifolds of the Fixed Point of a Second-Order Nonlinear Difference Equation
(Springer/plenum Publishers, 2020) Turan, Mehmet
This paper addresses the asymptotic approximations of the stable and unstable manifolds for the saddle fixed point and the 2-periodic solutions of the difference equationx(n+ 1)=alpha+beta x(n- 1)+x(n- 1)/x(n), where alpha> 0,0 <=beta<1$0\leqslant \beta and the initial conditionsx(- 1)andx(0)are positive numbers. These manifolds determine completely global dynamics of this equation. The theoretical results are supported by some numerical examples.
Citation - WoS: 1
Citation - Scopus: 1
The Truncated <i>q</I>-bernstein Polynomials in the Case <i>q</I> > 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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