Mehmet Turan

Original article: Bifurcation of discontinuous limit cycles of the Van der Pol equation

In this paper, we apply the methods of B-equivalence and @j-substitution to prove the existence of discontinuous limit cycle for the Van der Pol equation with impacts on surfaces. The result is extended through the center manifold theory for coupled oscillators. The main novelty of the result is that the surfaces, where the jumps occur, are not flat. Examples and simulations are provided to demonstrate the theoretical results as well as application opportunities.

The Limit q-Bernstein Operators with Varying q

In this paper, the continuity of the limit q-Bernstein operator with respect to parameter q is investigated. It is proved that the map q↦Bq is continuous in the strong operator topology on C[0, 1] for q ∈ [0, 1]. Meanwhile, in the uniform operator topology, this map is discontinuous at every q ∈ [0, 1].

On the Metric Space of the Limit q-Bernstein Operators

Abstract In this paper, some properties of uniformly discrete metric space are established. The metric ρ comes out naturally in the evaluation of the distance between two limit q-Bernstein operators with respect to the operator norm on The exact value of this distance is found for all Furthermore, a number of properties of metric bases in M are presented alongside all possible isometries on M.