The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

In this paper, we give a fixed point theorem for $(psi,varphi)$-weakly contractive mappings in complete $b$-metric spaces. We also give a common fixed point theorem for such mappings in complete $b$-metric spaces via altering functions. The given results generalize two known results in the setting of metric spaces. Two examples are given to verify the given results.

In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

By a hyperbolization of a locally compact non-complete metric space (X, d) we mean equipping X with a Gromov hyperbolic metric dh so that the boundary at infinity ∂∞X of (X, dh) can be identified with the metric boundary ∂X of (X, d) via a quasisymmetric map. The aim of this note is to show that the Gromov hyperbolic metric dh, recently introduced by the author, hyperbolizes the space X. In add...

The Baire theory of category, which classifies sets into two distinct categories, is an important topic in the study of metric spaces. Many results in topology arise from category theory; in particular, the Baire categories are related to a topological property. Because the Baire Category Theorem involves nowhere dense sets in a complete metric space, this paper first develops the concepts of n...

motivated by samet et al. [nonlinear anal., 75(4) (2012), 2154-2165], we introduce the notions of $alpha$-$phi$-fuzzy contractive mapping and $beta$-$psi$-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. the presented theorems extend, generalize and improve the corresponding results given in the literature.