The aim of this paper is to extend the Kannan fixed point theorem from single-valued self mappings T : X → X to mappings F : X3 → X satisfying a Prešić-Kannan type contractive condition: d (F (x, y, z) , F (y, z, u)) ≤ k 8 [d (x, F (x, y, z)) + d (y, F (y, x, y))+ +d (z, F (z, y, x)) + d (y, F (y, z, u)) + d (z, F (z, y, z)) + d (u, F (u, z, y))], or a Prešić-Chatterjea type contractive conditi...

In this paper, we study for some of the fixed point of mapping for a self map on a metric space under a contractive of integral type.

To each finite-dimensional operator space E is associated a commutative operator algebra UC(E), so that E embeds completely isometrically in UC(E) and any completely contractive map from E to bounded operators on Hilbert space extends uniquely to a completely contractive homomorphism out of UC(E). The unit ball of UC(E) is characterized by a Nevanlinna factorization and transfer function realiz...

Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how...

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...

Let φ be an isometric automorphism of the non-commutative disc algebra An for n ≥ 2. We show that every contractive covariant representation of (An, φ) dilates to a unitary covariant representation of (On, φ). Hence the C*-envelope of the semicrossed product An ×φ Z is On ×φ Z.

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.

The aim of this paper is to solve the fixed point problems : v = Ov, with Ov(x) def = max(Lv(x), Bv(x)), x ∈ E , (1) where E is a finite set, L is contractive and B is a nonexpansive operator and v = Ov, with Ov(x) def = max(sup w Lv(x), sup z Bv(x)), x ∈ E , (2) where W and Z are general control sets, the operators L are contractive and operators B are nonexpansive. For these two problems, we ...

and Applied Analysis 3 Again, using induction d xn 1, xn ≤ ( β 1 − α )n d x1, x0 , 2.5 Put k β/ 1 − α < 1. Moreover, by the triangular inequality, we have, form ≥ n, d xm, xn ≤ d xm, xm−1 d xm−1, xm−2 · · · d xn 1, xn ≤ ( km−1 km−2 · · · k ) d x1, x0 ≤ ( k 1 − k ) d x1, x0 , 2.6 and this proves that d xm, xn → 0 as m,n → ∞. So, {xn} is a Cauchy sequence and, since X is a complete metric space, ...