Sometimes there might be another metric space (N, ρ(u, v)) in play, and we may introduce a subscript as in BN(w, s) to indicate in which metric space the ball is defined. Let us say that a metric space (M, d(x, y)) is a happy fractal if the following three conditions are satisfied. First, M is complete as a metric space. Second, there is a constant C1 > 0 so that for each pair of points x, y in...

In this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. Our results generalize Kannan and Chatterjea fixed point theorems on complete $b$-metric spaces. In particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. We also give some examples to illustrate the given results.

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