A metric space is often represented as the pair (X,d). An example of metric spaces is (R, Lk), where Lk is the k-norm over R for given n, k ∈ Z≥1. We can represent a finite metric space (X, d) by a symmetric matrix S, of size nxn, where Si,j = d(i, j) and |X| = n. Metric spaces can be visualized using undirected graph G, where S is distance matrix for G. Conversely, given a graph G(V, E), we ca...

in the present paper, we give a new approach to caristi's fixed pointtheorem on non-archimedean fuzzy metric spaces. for this we define anordinary metric $d$ using the non-archimedean fuzzy metric $m$ on a nonemptyset $x$ and we establish some relationship between $(x,d)$ and $(x,m,ast )$%. hence, we prove our result by considering the original caristi's fixedpoint theorem.

1.1. Normed spaces. Recall that a (real) vector space V is called a normed space if there exists a function ‖ · ‖ : V → R such that (1) ‖f‖ ≥ 0 for all f ∈ V and ‖f‖ = 0 if and only if f = 0. (2) ‖af‖ = |a| ‖f‖ for all f ∈ V and all scalars a. (3) (Triangle inequality) ‖f + g‖ ≤ ‖f ||+ ‖g‖ for all f, g ∈ V . If V is a normed space, then d(f, g) = ‖f−g‖ defines a metric on V . Convergence w.r.t ...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

An axiom system for machine spaces is introduced. Time is modeled as a totally ordered monoid, thus allowing discrete, continuous, and transfinite time structures. A generalized metric on these machine spaces is defined, having values in a directedly ordered monoid. This enables the notion of ε-balls in machine space, which, for example, can be used to explore model risk and robustness in stati...

In this paper, a concept of monotone generalized contraction in partially ordered metric spaces is introduced and some fixed point and common fixed point theorems for the so-called weak contractions are proved. The concept of weak contraction was introduced by Kada, Suzuki and Takahashi [Math. Japonica, 44 (1996), 381-391], in connection to the concept of w-distance on a metric space. The resul...

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an invariant metric on X. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and local...

Proving  fixed point theorem in a fuzzy metric space is not possible for  Meir-Keeler contractive mapping. For this, we introduce the notion of $c_0$-triangular fuzzy metric space. This new space allows us to prove some fixed point theorems for  Meir-Keeler contractive mapping. As some pattern we introduce the class of $alphaDelta$-Meir-Keeler contractive and we establish some results of fixed ...

Abbas M, Arsad M, Azam A (2013), Fixed points of asymptotically regular mappings in complex-valued metric spaces, Georgian Math. J. , 20 (2), 213-221. Abbas M. Fisher B, Nazir T (2012), Well-posedness and periodic point property of mappings satisfying a rational inequality in an ordered complex valued metric space, Sci. Stud. Res. , Ser. Math. Inform. , 22 (1), 5-24. Ahmad J, Klin-Eam C, Azam A...

Abbas M, Arsad M, Azam A (2013), Fixed points of asymptotically regular mappings in complex-valued metric spaces, Georgian Math. J. , 20 (2), 213-221. Abbas M. Fisher B, Nazir T (2012), Well-posedness and periodic point property of mappings satisfying a rational inequality in an ordered complex valued metric space, Sci. Stud. Res. , Ser. Math. Inform. , 22 (1), 5-24. Ahmad J, Klin-Eam C, Azam A...