TVS-cone metric spaces as a special case of metric spaces

There have been a number of generalizations of fixed point results to the so called TVS-cone metric spaces, based on a distance function that takes values in some cone with nonempty interior (solid cone) in some topological vector space. In this paper we prove that the TVS-cone metric space can be equipped with a family of mutually equivalent (usual) metrics such that the convergence (resp. property of being Cauchy sequence, contractivity condition) in TVS sense is equivalent to convergence (resp. property of being Cauchy sequence, contractivity condition) in all of these metrics. As a consequence, we prove that if a topological vector space $E$ and a solid cone $P$ are given, then the category of TVS-cone metric spaces is a proper subcategory of metric spaces with a family of mutually equivalent metrics (Corollary 3.9). Hence, generalization of a result from metric spaces to TVS-cone metric spaces is meaningless. This, also, leads to a formal deriving of fixed point results from metric spaces to TVS-cone metric spaces and makes some earlier results vague. We also give a new common fixed point result in (usual) metric spaces context, and show that it can be reformulated to TVS-cone metric spaces context very easy, despite of the fact that formal (syntactic) generalization is impossible. Apart of main results, we prove that the existence of a solid cone ensures that the initial topology is Hausdorff, as well as it admits a plenty of convex open sets. In fact such topology is stronger then some norm topology.Comment: 14 page

Common fixed points of noncommuting almost contractions in cone metric spaces

In this paper we prove the existence of coincidence points and common fixed points for a large class of almost contractions in cone metric spaces. These results generalize, extend and unify several well-known recent related results in literature

Coincidence Point with Application to Stability of Iterative Procedure in Cone Metric Spaces

We obtain necessary conditions for the existence of coincidence point and common fixed point for contractive mappings in cone metric spaces. An application to the stability of J-iterative procedure for mappings having coincidence point in cone metric spaces is also given

Common Fixed Points For Three Maps In Cone Metric Spaces

The existence of coincidence points and common fixed point theorem for three maps satisfying certain contractive conditions without exploiting the notation of continuity of any map involved therein cone metric space is proved . Our  result  extends and generalize some recent  results . Keywords: Cone metric space , Common Fixed Point ,  Coincidence point

Some common fixed point results of three self-mappings in cone metric spaces

The aim of this paper is to present coincidence point and common fixed point results for three self mappings satisfying generalized contractive conditions.  The results presented in this paper generalize and extend several well-known results in the literature

Some Common Fixed Point Results in Cone Metric Spaces

We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results