the purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in banach spaces. our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).

Let E be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let J {T t : t ≥ 0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of E, with functions u, v : 0,∞ → 0,∞ . Let F : F J ∩t≥0F T t / ∅ and f : K → K be a weakly contractive map. For some positive real numbers λ and δ satisfying δ λ > 1, let G ...

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...

A signed graph has edge weights drawn from the set $\{+1,-1\}$, and is termed sign-balanced if it equivalent to an unsigned under operation of sign switching; otherwise called sign-unbalanced. nut a one dimensional kernel with corresponding eigenvector that full. In this paper we generalise notion graphs graphs. Orders for which regular exist were determined recently degrees up $11$. By extendi...

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Hoffman, Wolfe, and Ho...

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K → K be an I-asymptotically quasi-nonexpansive type mapping and I : K → K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type ma...

Given a finite generating set $T=\{g_0,\dots, g_n\}$ of group $G$, and representation $\rho$ $G$ on Hilbert space $V$, we investigate how the geometry $D(T,\rho)=\{ [x_0 : \dots x_n] \in\mathbb C\mathbb P^n \mid \sum x_i\rho(g_i) \text{ not invertible} \}$ reflects properties $\rho$. When $V$ is finite-dimensional this an algebraic hypersurface in $\mathbb P^n$. In special case $T=G$ $\rho=$ le...

In this paper we prove that random d–regular graphs with d ≥ 3 have traffic congestion of the order O(n log3d−1(n)) where n is the number of nodes and geodesic routing is used. We also show that these graphs are not asymptotically δ–hyperbolic for any non–negative δ almost surely as n→∞.

In 2006, Barát and Thomassen conjectured that the edges of every planar 4-regular 4-edgeconnected graph can be decomposed into claws. Shortly afterward, Lai constructed a counterexample to this conjecture. Using the small subgraph conditioning method of Robinson and Wormald, we find that a random 4-regular graph has a claw-decomposition asymptotically almost surely, provided that the number of ...