A nonlinear control system is said to be weakly contractive in the if flow that it generates non-expanding (in sense distance between two trajectories a non-increasing function of time) for some fixed Riemannian metric independent control. We prove this paper such systems, local asymptotic stabilizability implies global by means dynamic state feedback. link result and so-called Jurdjevic Quinn ...

The A-proper class arises naturally when one considers the approximation solvability of nonlinear equations, that is, obtaining solutions of infinite-dimensional problems as limits of solutions of related finite-dimensional problems. The class was first introduced by Petryshyn, who made many important contributions to the theory, see, for example, [17, 18] for a good account of this. The A-prop...

for all x, y ∈ X. Kannan [] proved that if X is complete, then a Kannan mapping has a fixed point. It is interesting that Kannan’s theorem is independent of the Banach contraction principle []. Also, Kannan’s fixed point theorem is very important because Subrahmanyam [] proved that Kannan’s theorem characterizes the metric completeness. That is, a metric space X is complete if and only if ev...

In this article, we discuss the relation-theoretic aspects of weakly contractive mappings to prove fixed point results in setting metric spaces endowed with a certain binary relation. We also provide an example and application validate our results. The proved herewith unify, generalize, improve, extend, sharpen, subsume enrich some well-known theorems existing literature.

We are concerned with function approximation and image representation using Iterated Function Systems (IFS) over L p (X;): An N-map IFS with grey level maps (IFSM), to be denoted as (w;), is a set w of N contraction maps w i : X ! X over a compact metric space (X; d) (the \base space") with an associated set of maps i : R ! R. Associated with each IFSM is a contractive operator T with xed point...

By use of a new viscosity approximation method, we construct an explicit iterative algorithm for finding common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in the framework of Banach spaces. A strong convergence theorem is obtained for solving a kind of variational inequality problems. Our results improve and extend the corresponding ones of other author...

We construct random iterative processes for weakly contractive and asymptotically nonexpansive random operators and study necessary conditions for the convergence of these processes. It is shown that they converge to the random fixed points of these operators in the setting of Banach spaces. We also proved that an implicit random iterative process converges to the common random fixed point of a...

The purpose of this paper is to study the convergence problem of Mann and Ishikawa type iterative schemes of weakly contractive mapping in a complete convex metric space. We establish the results on invariant approximation for the mapping defined on a class of nonconvex sets in a convex metric space. Finally, we obtain the existence of common fixed points of two asymptotically nonexpansive mapp...