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

The Results on Coincidence and Common Fixed Points for a New Type Multivalued Mappings in b-Metric Spaces

In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces. We work with a new type of multivalued quasi-contractive mapping with nonlinear comparison functions. Our results generalize and improve several recent results. Additionally, we give an application of the obtained results to dynamical systems

Matching theorems on topological spaces

In this paper we give one general matching theorem and some its applications in the fixed point theory. Our results generalize earlier theorems obtained by Horvath, Chang - Zhang and Chang - Ma

On Boyd-Wong-type fixed point results

This talk (paper) gives a survey of recent results in the theory of Boyd-Wong-type contractions and its aim is to present a simple and unified treatment to this theory. In final part of paper, we present one recent fixed point result for Boyd-Wong-type contractions defined on symmetric spaces

On Boyd-Wong-type fixed point results

This talk (paper) gives a survey of recent results in the theory of Boyd-Wong-type contractions and its aim is to present a simple and unified treatment to this theory. In final part of paper, we present one recent fixed point result for Boyd-Wong-type contractions defined on symmetric spaces

An inequality for the Lebesgue measure and its further applications

In [Univ. Beograd Publ. Elektrotehn. Fak. Ser. Math. 15 (2004), 85-86], the first author of this paper proved a new inequality for the Lebesgue measure and gave some applications. Here, we present a new application of this inequality.

An inequality for the Lebesgue measure and its further applications

In [Univ. Beograd Publ. Elektrotehn. Fak. Ser. Math. 15 (2004), 85-86], the first author of this paper proved a new inequality for the Lebesgue measure and gave some applications. Here, we present a new application of this inequality.

An inequality for the Lebesgue measure

In this paper we present a new inequality for the Lebesgue measure and give some of its applications