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.

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...

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.

A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines This property implies highly ordered asymptotic behavior including entrainment to time-varying periodic vector fields and, in particular, global stability for time-invariant fields. Contraction theory has found numerous applications systems and ...