Metric spaces with unique pretangent

Fixed Point Theory and Applications, 2013

In this paper, we first introduce two new classes of (ω, δ)-contractions of the first and second kinds and establish some related new fixed point and best proximity point theorems in preordered metric spaces. Our theorems subsume the corresponding recent results of Samet (J.

Fixed Point Theory and Applications, 2014

Inspired by the notion of Mustafa and Sims' G-metric space and the attention that this kind of metric has received in recent times, we introduce the concept of a G-metric space in any number of variables, and we study some of the basic properties. Then we prove that the family of this kind of metric is closed under finite products. Finally, we show some fixed-point theorems that improve and extend some well-known results in this field. MSC: 46T99; 47H10; 47H09; 54H25

2010

We obtained related fixed point theorem on three metric spaces.

2011

A Smarandache multi-space is a union of n spaces A 1 , A 2 , • • • , A n with some additional conditions holding. Combining Smarandache multispaces with classical metric spaces, the conception of multi-metric space is introduced. Some characteristics of a multi-metric space are obtained and Banach's fixed-point theorem is generalized in this paper.

In this paper we establish some common fixed point results for two self-mappings f and g on a universal metric space of dimension n. To prove our results we assume that f is a weakly U-contraction mapping of types A u and B u with respect to g. Also we introduce a new concept Γ-distance on a complete partially ordered U n-metric space and prove a fixed point theorem.

arXiv (Cornell University), 2022

Richmond and Richmond (American Mathematical Monthly 104 (1997), 713-719) proved the following theorem: If, in a metric space with at least five points, all triangles are degenerate, then the space is isometric to a subset of the real line. We prove that the hypothesis is unnecessarily strong: In a metric space on n points, n 3n + 5 arbitrarily placed or 3 n-2 2 + 1 suitably placed degenerate triangles suffice. 1 Results. Given a metric space (V, dist), we follow [1] in writing [rst] to signify that r, s, t are pairwise distinct points of V and dist(r, s) + dist(s, t) = dist(r, t). Following , we refer to three-point subsets of V as triangles; if [rst], then the triangle {r, s, t} is called degenerate. Now let (V, dist) be a metric space. Trivially, if there is a linear order on V such that r ≺ s ≺ t ⇒ [rst], then all triangles in V are degenerate. Richmond and Richmond [15] proved the converse under a mild lower bound on |V |:

Nonlinear functional analysis and applications, 2018

In this paper, we prove some topological properties and a common fixed point type theorem for two self mappings on new generalized metric spaces, called A−metric spaces.

Fixed Point Theory and Applications, 2013

The purpose of this paper is to prove some fixed point theorems in a complete metric space equipped with a partial ordering using w-distances together with the aid of altering functions. MSC: 54H25; 47H10

2006

We present a survey of fixed point results in generalized metric spaces (g.m.s.) in the sense of Branciari , A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57, 31-37]. Since it may happen that the topology of such space is not Hausdorff, several authors added Hausdorfness (or some other condition) as an additional assumption in order to obtain their results. We show here that such assumptions are usually superfluous. Finally, we state some open questions on the topic.

We introduce a new concept of generalized metric spaces and extend some well-known related fixed point theorems including Banach contraction principle, Ćirić's fixed point theorem, a fixed point result due to Ran and Reurings, and a fixed point result due to Nieto and Rodríguez-López. This new concept of generalized metric spaces and extend some well-known related fixed point theorems recover various topological spaces including standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces.

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 metric-like space. In this study, we define the diameter of a subset of a metric-like space, and then we provide a definition for bounded subsets of a metric-like space. In line with the aforemen-tioned issues, various examples are provided to better understand this space.

Advances in the Theory of Nonlinear Analysis and its Application, 2017

This is a survey of results mainly in metric fixed point theory, including the Darbo-Sadovskiȋ theorem using measures of noncompactness. Various different proofs are presented for some of the most important historical results. Furthermore many examples and remarks are added to illustrate the topics of the paper.

2006

To overcome fundamental flaws in B. C. Dhage's theory of generalized metric spaces, flaws that invalidate most of the results claimed for these spaces, we introduce an alternative more robust generalization of metric spaces. Namely, that of a G-metric space, where the G-metric satisfies the axioms: (1) G(x, y, z) = 0 if x = y = z; (2) 0 < G(x, x, y) ; whenever x =/= y, (3) G(x, x, y) <= G(x, y, z) whenever z =/= y, (4) G is a symmetric function of its three variables, and (5) G(x, y, z) <= G(x, a, a) + G(a, y, z).

Computational & Applied Mathematics

In this paper we consider some new definitions about quadrupled fixed point in abstract metric spaces and obtain some new fixed point results in this field. These results unify, extend and generalize well-known comparable results in the existing literature. We also provide some examples and applications to support our results.