Annals of Probability 31(2003), 2109-2135. Invariant man-ifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invarian...

*Correspondence: [email protected] 1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and...

Consider the holiday season, where there are n players who would like to exchange gifts. That is, we would like to generate a random permutation having no fixed point. It is known that such a random permutation can be obtained in a hidden form by using a number of physical cards of four colors with identical backs, guaranteeing that it has no fixed point (without revealing the permutation itsel...

In this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of F -invariant set. We introduce the notion of fixed point of N -order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement...