Graph Echo State Networks (GraphESN) extend the Reservoir Computing approach to directly process graph structures. The reservoir is applied to every vertex of an input graph, realizing a contractive encoding process and resulting in a structured state isomorphic to the input. Whenever an unstructured output is required, a state mapping function maps the structured state into a fixed-size featur...

The main objective of this paper is to deal with some properties of interest in two types of fuzzy ordered proximal contractions of cyclic self-mappings T integrated in a pair (g, T) of mappings. In particular, g is a non-contractive fuzzy self-mapping, in the framework of non-Archimedean ordered fuzzy complete metric spaces and T is a p-cyclic proximal contraction. Two types of such contractio...

A general method is developed to obtain conditions on initial data and forcing terms for the global existence of unique regular solutions to incompressible 3d Navier-Stokes equations. The basic idea generalizes a probabilistic approach introduced by LeJan and Sznitman (1997) to obtain weak solutions whose Fourier transform may be represented by an expected value of a stochastic cascade. A funct...

We find concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size 4×4 in the extremal case. Along the way we introduce a new approach that allows us to solve, algorithmically, the contractive completion problem for 4 × 4 Hankel matrices. As an application, we obtain a concrete example of a partially contractive 4× 4 Hankel m...

Barnsley (2006) introduced the notion of a fractal top, which is an addressing function for the set attractor of an Iterated Function System (IFS). A fractal top is analogous to a set attractor as it is the fixed point of a contractive transformation. However, the definition of IFS is extended so that it works on the colour component as well as the spatial part of a picture. They can be used to...

We can see from (p) and (p) that p(x, y) =  implies x = y. However, the converse is not necessarily true. A typical example of this situation is provided by the partial metric space (R,pmax), where the function pmax : R+ × R+ → R+ is defined by pmax(x, y) =max{x, y} for all x, y ∈ R+. Other examples of partial metric spaces which are interesting from a computational point of view may be foun...

Let C be a closed convex subset of a uniformly smooth Banach space E, and T : C → E a nonexpansive nonself-mapping satisfying the weakly inwardness condition such that F(T) = ∅, and f : C → C a fixed contractive mapping. For t ∈ (0,1), the implicit iterative sequence {xt} is defined by xt = P(t f (xt) + (1− t)Txt), the explicit iterative sequence {xn} is given by xn+1 = P(αn f (xn) + (1−αn)Txn)...

*Correspondence: [email protected] 1Instituto de Investigacion y Desarrollo de Procesos, Universidad del Pais Vasco, Campus of Leioa (Bizkaia), Aptdo. 644, Bilbao, Bilbao 48080, Spain Full list of author information is available at the end of the article Abstract This paper discusses three contractive conditions for two 2-cyclic self-mappings defined on the union of two nonempty subsets of ...

The fixed point theorems in metric spaces are playing a major role to construct methods in mathematics to solve problems in applied mathematics and sciences. So the attraction of metric spaces to a large numbers of mathematicians is understandable. Some generalizations of the notion of a metric space have been proposed by some authors. In 2006, Mustafa in collaboration with Sims introduced a ne...

Our aim in the present paper is three fold. Firstly, we obtain a common fixed point theorem for a pair of self mappings satisfying a Lipschitz type condition employing the property (E.A.) along with a relatively new notion of absorbing pair of maps wherein we never require conditions on the completeness of the space, containment of range of one mapping into the range of other, continuity of the...