1. INTRODUCTION. When studying a metric space, it is valuable to have a mental picture that displays distance accurately. When the space is Z, Q, or R, we usually form such a picture by imagining points on the " number line ". When the space is X = Z 2 , Q 2 , R 2 , or C we use a planar picture in which nonempty discs (sets of the form {x ∈ X : d(x, b) ≤ γ } or {x ∈ X : d(x, b) < β}, with metri...

in this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is riesz space valued. we prove some common fixed point theorems for three mappings in this space. obtained results extend and generalize well-known comparable results in the literature.

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...

In this paper, we introduce a new class of contractive mappings in a fuzzy metric space and we present fixed point results for this class of maps.

in this paper, we generalize fuzzy banach contraction theorem establishedby v. gregori and a. sapena [fuzzy sets and systems 125 (2002) 245-252]using notion of altering distance which was initiated by khan et al. [bull. austral.math. soc., 30(1984), 1-9] in metric spaces.

in this paper, we introduce a new class of implicit functions and also common property (e.a) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. we are not aware of any paper dealing with such implicit functions in modified intuit...

we consider the concept of ω-distance on a complete partially ordered g-metric space and prove some common fixed point theorems.