On Order-Convergence

On Order-convergence

A Note on Q-order of Convergence

To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. A new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-o...

Second Order Sliding Mode Control With Finite Time Convergence

In this paper, a new smooth second order sliding mode control is proposed. This algorithm is a modified form of Super Twisting algorithm. The Super Twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular Lyapunov function. The Proposed algorithm which is able to control nonlinear systems with matched structured u...

On $I$-statistical and $I$-lacunary statistical convergence of order $alpha$

In this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$I$-statistical convergence and‎ ‎$I$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{N}$) and‎ ‎introduce the notions of $I$-statis...

First-Order Convergence and Roots

Nešetřil and Ossona de Mendez introduced the notion of first order convergence, which unifies the notions of convergence for sparse and dense graphs. They asked whether if (Gi)i∈N is a sequence of graphs with M being their first order limit and v is a vertex of M , then there exists a sequence (vi)i∈N of vertices such that the graphs Gi rooted at vi converge to M rooted at v. We show that this ...