In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metr...

in this paper we discuss on the fixed points of asymptotic contractions and boyd-wong type contractions in uniform spaces equipped with an e-distance. a new version ofkirk's fixed point theorem is given for asymptotic contractions and boyd-wong type contractions is investigated in uniform spaces.

Let T be a periodic time scale. We use a fixed point theorem due to Krasnosel’skĭı to show that the nonlinear neutral dynamic equation with delay x(t) = −a(t)x(t) + (Q(t, x(t), x(t− g(t))))) +G ` t, x(t), x(t− g(t)) ́ , t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the aid ...

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state.

By introducing a new concept called ‘‘set-valued asymptotic contraction’’ in metric spaces, the existence and uniqueness of endpoints for a set-valued asymptotic contraction which has the approximate endpoint property have been established. © 2010 Elsevier Ltd. All rights reserved.

Let T be a periodic time scale. We use a fixed point theorem due to Krasnoselskii to show that the nonlinear neutral dynamic equation with infinite delay x(t) = −a(t)x(t) + (Q(t, x(t− g(t))))) + ∫ t −∞ D (t, u) f (x(u)) ∆u, t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the...

in this paper, we introduce the (g-$psi$) contraction in a metric space by using a graph.let $f,t$ be two multivalued mappings on $x.$ among other things, we obtain a common fixedpoint of the mappings $f,t$ in the metric space $x$ endowed with a graph $g.$