THE NEARLY ADDITIVE MAPS

On the additive maps satisfying Skew-Engel conditions

Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:Irightarrow R$ be an additivemap. Then skew-Engel condition $langle... langle langle$$f(x),x^{n_1} rangle,x^{n_2} rangle ,...,x^{n_k} rangle=0$ implies that $f (x)=0$ $forall,xin I$ provided $2neq$ char $(R)>n_1+n_2+...+n_k, $ where $n_1,n_2,...,n_k$ are natural numbers. This extends some existing results. In the end, we also gener...

Nearly Euclidean Thurston Maps

We take an in-depth look at Thurston’s combinatorial characterization of rational functions for a particular class of maps we call nearly Euclidean Thurston maps. These are orientation-preserving branched maps f : S2 → S2 whose local degree at every critical point is 2 and which have exactly four postcritical points. These maps are simple enough to be tractable, but are complicated enough to ha...

On The Convergence Of Modified Noor Iteration For Nearly Lipschitzian Maps In Real Banach Spaces

In this paper, we obtained the convergence of modified Noor iterative scheme for nearly Lipschitzian maps in real Banach spaces. Our results contribute to the literature in this area of re- search.

On Nearly Euclidean Thurston Maps

Additive Spanners in Nearly Quadratic Time

We consider the problem of efficiently finding an additive C-spanner of an undirected unweighted graph G, that is, a subgraph H so that for all pairs of vertices u, v, δH(u, v) ≤ δG(u, v) + C, where δ denotes shortest path distance. It is known that for every graph G, one can find an additive 6-spanner with O(n) edges in O(mn) time. It is unknown if there exists a constant C and an additive C-s...