Let $T\colon L^p({\mathcal M})\to N})$ be a bounded operator between two noncommutative $L^p$-spaces, $1\leq p<\infty$. We say that $T$ is $\ell^1$-bounded (resp. $\ell^1$-contractive) if $T\otimes I_{\ell^1}$ extends to contractive) map from $L^p({\mathcal M};\ell^1)$ into N};\ell^1)$. show Yeadon's factorization theorem for $L^p$-isometries, p\not=2 <\infty$, applies an isometry L^2({\mathcal...

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The...

We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented with functions yielding components for a p-basis and a chain of subgroups indexed by the valuation group.

Rhoades (1996) proved a fixed point theorem in a bounded D-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unbounded D-metric space, for two self-maps satisfying a general contractive condition with a restricted domain of x and y. This has been done by using the notion of semicompatible maps in D-metric space. These results g...

The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of conditional reciprocal continuity. We demonstrate that conditional reciprocal continuity ensures the existence of fixed points under contractive conditions which otherwise do not ensure the existence of fixed points. Our results generalize and extend several well-known fixed poin...

A contraction analysis of risk-sensitive Riccati equations is proposed. When the state-space model is reachable and observable, a block-update implementation of the risk-sensitive filter is used to show that the N-fold composition of the Riccati map is strictly contractive with respect to the Riemannian metric of positive definite matrices, when N is larger than the number of states. The range ...

Meir and Keeler in 1 considered an extension of the classical Banach contraction theorem on a complete metric space. Kirk et al. in 2 extended the Banach contraction theorem for a class of mappings satisfying cyclical contractive conditions. Eldred and Veeramani in 3 introduced the following definition. Let A and B be nonempty subsets of a metric space X. A map T : A ∪ B → A ∪ B, is a cyclic co...

Osteopathy in thalassemia is a very heterogeneous condition; severity depends on multiple factors, interacting through nonlinear mechanisms. Classic statistics have limitations when applied to the study of such highly complex relationships. Currently, an alternative approach of analysis is represented by the artificial neural networks (ANNs), powerful mathematical tools, increasingly applied to...

The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a TVS-valued cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature.

Let X, d be a complete metric space, and let T be a self-map of X. If T has a unique fixed point, which can be obtained as the limit of the sequence {pn}, where pn Tp0, p0 any point of X, then T is called a Picard operator see, e.g., 1 , and the iteration defined by {pn} is called Picard iteration. One of the most general contractive conditions for which a map T is a Picard operator is that of ...