We prove that if a sequence of graphs has (asymptotically) the same distribution of small subgraphs as a generalized random graph modeled on a fixed weighted graph H, then these graphs have a structure that is asymptotically the same as the structure of H. Furthermore, it suffices to require this for a finite number of subgraphs, whose number and size is bounded by a function of |V (H)|.

In other words, when (u; u(0N); 11 1;u(01)) belongs to U , asymptotically periodic inputs produce asymptotically periodic outputs with the same period. The proof of this theorem makes use of a contraction-mapping fixed-point argument. The techniques used in our omitted proofs are also useful in connection with related problems that are " more nonlinear. " In particular, related results are give...

Given an unknown signal x0 ∈ R and linear noisy measurements y = Ax0 + σv ∈ R, the generalized `2-LASSO solves x̂ := argminx 12‖y −Ax‖ 2 2 + σλf(x). Here, f is a convex regularization function (e.g. `1-norm, nuclearnorm) aiming to promote the structure of x0 (e.g. sparse, lowrank), and, λ ≥ 0 is the regularizer parameter. A related optimization problem, though not as popular or well-known, is of...

It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...

Let K be a convex subset of a uniformly convex Banach space. It is proved that if K is compact, then the fixed points of a continuous generalized nonexpansive self-mapping T on K can be approximated by the iterates of T, with t B (0,1), T,(x) = (1 t)x + tT(x), x e K; T, is asymptotically regular if T has a fixed point. Let (X, d) be a (nonempty) metric space. A function a of X X X into [0, oo) ...

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...