This probably doesn’t deserve a § all to itself, but it will be handy to know it in what follows. Recall that a set S in a metric (or topological) space X is dense-in-itself 1 if every neighborhood of each s0 ∈ S contains points s ∈ S different from s0. One says that S is perfect if it is closed and dense-in-itself. A topological (or metric) space is separable if it has a countable subset whose...

In this paper, the notion of $psi -$weak contraction cite{Rhoades} isextended to fuzzy metric spaces. The existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. Our resultgeneralizes a result of Gregori and Sapena cite{Gregori}.

In this paper is introduced a new type of generalization of metric spaces called $S_b$ metric space. For this new kind of spaces it has been proved a common fixed point theorem for four mappings which satisfy generalized contractive condition. We also present example to confirm our theorem.

Q × ́ and induces a metric topology in this group. We show that the completion of this metric space is a Banach space over the field R of real numbers. We further show that this Banach space is isometrically isomorphic to a co-dimension one subspace of L(Y,B, λ), where Y is a certain totally disconnected, locally compact space, B is the σ-algebra of Borel subsets of Y , and λ is a certain measur...

In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally $G$-continuity of mapping and we consider $b$-metric spaces with graph instead of $b$-metric spaces, under which can be gen...

This study involves new notions of continuity mapping between quasi-cone metrics spaces (QCMSs), cone metric (CMSs), and vice versa. The relation all were thoroughly studied supported with the help examples. In addition, these continuities compared various types two QCMSs. are

In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...

Remark. The non-archimedean topology: Recall that if K is a field with a val­ uation | |, then it also is a metric space with d(x, y) = |x − y|. The topology has a basis of open neighborhoods given by B(x, ǫ) = {y ∈ K | |x − y| < ǫ}. If the valuation is nonarchimedean, then this metric space or topology is rather bizarre. For instance, the open balls don’t have a unique center: in fact, if we t...

in this paper, we study a special class of generalized douglas-weyl metrics whose douglas curvature is constant along any finslerian geodesic. we prove that for every landsberg metric in this class of finsler metrics, ? = 0 if and only if h = 0. then we show that every finsler metric of non-zero isotropic flag curvature in this class of metrics is a riemannian if and only if ? = 0.