Families of quasipseudometrics generated by probabilistic quasipseudometric spaces mariusz t. Fixed point results in dislocated quasi metric spaces. We also demonstrate that the main results of the paper cover several existing results in the literature. Some new observations on geraghty and ciric type results in. Dislocated quasibmetric spaces and fixed point theorems. Quasimetric spaces transition systems prevision transition systems add action labels 2l, to control system. We establish convergence theorems of a sequence in quasimetric spaces.
Pdf contribution of fixed point theorem in quasi metric. The banach contraction principle forms the basis of metric fixed point theory. Notes on metric spaces these notes introduce the concept of a metric space, which will be an essential notion throughout this course and in others that follow. They called a t 0quasimetric space qhyperconvex if and only if it is injective in the category of t 0. Completely metrizable spaces can be characterized as those spaces that can be written as an intersection of countably many open subsets of some complete metric space. Fixed point theorems in dislocated quasi d metric spaces.
Bicompleting weightable quasimetric spaces and partial. Wait m 1 m 2 init insertcoin cancel insertcoin cancel pressbutton servecoffee cashin serving served l is a set ofactionsthatphas control over. A new generalized quasi metric space with some fixed. Since quasi metric spaces form a generalization of metric spaces, any sound completion theory for such. Introduction some convergence theorems of certain iterations to a. With the help of a suitable modification of its proof, we deduce a characterization of smyth complete quasimetric spaces which provides a quasimetric generalization of the wellknown characterization of metric completeness due to kirk. Hans triebel a new approach to function spaces on quasimetric spaces where. Mathematics free fulltext modified suzukisimulation. Sets of biological sequences with some commonly used similarity. Xxxr is called a metric or distance function if ad only if. We obtain a quasimetric generalization of caristis fixed point theorem for a kind of complete quasimetric spaces. Further, this theorem is used to generalize caristis fixed point theorem and ekelands.
Completely metrizable spaces are often called topologically complete. In this paper, we prove some best proximity point theorems for ordered rational proximal contractions of. Pdf on generalized quasi metric spaces researchgate. While many constructions from the metric case carry through to the quasimetric case without much change, some quasimetric results have only trivial analogs. Fixed point results for different types of contractive conditions are established, which generalize, modify and unify some existing fixed point theorems in the literature. We show that the bicompletion of a weightable quasimetric space is a weightable quasimetric space. In, mustafa and sims introduced the concept of a gmetric space as a generalized metric space. If x,d is a metric space and a is a nonempty subset of x, we can make a metric d a on a by putting. The purpose of this note is to improve stoltenbergs theorem. There are many ways to make new metric spaces from old.
Pdf a quasimetric is a distance function which satisfies the triangle inequality but is not symmetric in general. We show that this concept leads to similar results as in the metric case and we prove that the most important spaces of computable analysis can be naturally considered as recursive quasimetric spaces. A notion of cauchy sequence in quasimetric spaces is introduced and used to define a standard completion for a special class of spaces. In this paper, we establish dislocated quasibmetric spaces and introduce the notions of geraghty type dqbcyclicbanach contraction and dqbcyclickannan mapping and derive the existence of fixed point theorems for such spaces. On completeness in quasimetric spaces sciencedirect. The definitions proposed allow versions of such classical theorems as the baire category theorem, the contraction principle and cantors characterization of completeness to be formulated in the quasipseudometric setting. Metric spaces a metric space is a set x that has a notion of the distance dx,y between every pair of points x,y. Quasiisometries kevin whyte berkeley fall 2007 lecture 1 theorem 1. Since the conclusion of the baire category theorem is purely topological, it applies to these spaces as well. A new concept in dislocated and dislocated quasi metric.
Quasimetric tree in t0quasimetric spaces sciencedirect. Finally, we acquired graphical fixed point results in nonarchimedean quasi modular metric spaces. A new approach to function spaces on quasimetric spaces. Since such spaces are quasimetrizable but nonmetrizable, we will need to develop our theory in the realm of quasimetric spaces. Department of mathematics, university of leicester, leicester, lei 7rh. Isufati 1 proved fixed point theorems for a single map and a pair of mappings in dislocated metric spaces. These questions are subsumed by computing simulation hemimetrics between 1 and. We prove a new minimization theorem in quasimetric spaces, which improves the results of takahashi 1993. Some fixed point results in dislocated quasi metric dq. On completeness in quasimetric spaces introduction core. Many authors invented the generalizations of metric spaces by various ways and established the contraction mapping theorem in it. Pdf quasi metrics have been used in several places in the literature on domain theory and the formal semantics of programming languages. We extend some of the mmspace concepts to the setting of a quasi. A metric induces a topology on a set, but not all topologies can be generated by a metric.
Introduction let x be an arbitrary set, which could consist of vectors in rn, functions, sequences, matrices, etc. We also have the following simple lemma lemma 3 a subset u of a metric space is open if and only if it is a neighbor hood of each of its points. After that, many fixed point theorems on gmetric spaces were. From this result we deduce that any partial metric space has an up to isometry unique partial metric bicompletion. In particular, applications to two interesting examples of partial metric spaces which appear in computer science, as the domain of. Fixed point theorems for ciric type contractions in. If g acts geometrically on x and y proper geodesic metric spaces then x and y are quasiisometric. Mlaiki, nabil dedovic, nebojsa aydi, hassen gardasevicfilipovic, milanka binmohsin, bandar and radenovic, stojan 2019. Some properties and applications of fuzzy quasipseudometric spaces sorin nadaban1, ioan dzitac1,2. Note that iff if then so thus on the other hand, let. Fixed point theorems in quasi metric spaces and applications to multidimensional fixed point theorems on g metric spaces article in journal of nonlinear and convex analysis 169.
A geometric action is a group action that is cocompact, isometric, and properly discontinuous. Using this new concept, a fixedpoint theorem is established. This study showed that fixed point theorems for two mappings in quasi jsmetric spaces were proved. Reasonably, we want to repair this situation, and in as economical way as possible. Second, in, we constituted a new quasi metric space, which is named the nonarchimedean quasi modular metric space, and so using this, we attained fixed point theorems via generalized suzukisimulationtype contractive mapping. A few examples of generalized metric spaces are quasi metric spaces, cone metric spaces,gmetric spaces, dislocated metric spaces,bmetric. Dhage 2 introduced the concept of d metric spaces and proved several fixed point theorems in it.
Cauchy sequences in quasipseudometric spaces springerlink. Bag abstract the skeleton of this manuscript consists of a concept of compact quasimetric space and some fundamental behaviors of this space. We also provide an example verifying and illustrating the fixedpoint theorem in action. A topological space whose topology can be described by a metric is called metrizable an important source of metrics in differential. Quasicontractions on metric spaces 325 for all x,y in x for which the righthand side of the inequality is positive. Pdf the geodesic problem in quasimetric spaces qinglan. We do not develop their theory in detail, and we leave the veri. T,quasimetric space x, d has to be defined in such a manner that the following requirements are fulfilled.
This paper contains a study of families of quasipseudometrics the concept of a quasipseudometric was introduced by wilson 22, albert 1 and kelly 9 generated by proba bilistic quasipseudometricspaces which are generalization of probabilistic metric space pmspace shortly 2, 3, 4, 6. On the moduli spaces of leftinvariant pseudoriemannian metrics on lie groups kubo, akira, onda, kensuke, taketomi, yuichiro, and tamaru, hiroshi, hiroshima mathematical journal, 2016. It is clear that b metric spaces, quasib metric spaces and b metriclike spaces are dqb metric spaces but converse is not true. We introduce a novel approach towards harnacks inequality in the context of spaces of homogeneous type. In this paper, the notions of ciric type i contractions and ciric type ii contractions in generating spaces of quasimetric family are introduced and new fixed point theorems for such two contractions are established. Some of this material is contained in optional sections of the book, but i will assume none of that and start from scratch. This paper considers the problem of defining cauchy sequence and completeness in quasipseudometric spaces. In this paper, we introduce the concept of a setvalued or multivalued quasicontraction mapping in v fuzzy metric spaces. We consider examples to illustrate the main results. We dene continuous function and prove generalized weierstrass theorem in this work. The aim of this paper is to investigate some fixed point results in dislocated quasi metric dqmetric spaces. Pdf the purpose of this work is to study topological properties of bdislocated quasimetric space and derive some fixed point theorems.
Pdf on statistical convergence in quasimetric spaces. Metric spaces are first countable since one can use balls with rational radius as a neighborhood base. In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set. In this paper we study on contribution of fixed point theorem in metric spaces and quasi metric spaces. Then the pair x,d is called dislocated quasi bmetric space or in short dqb metric space. It is not hard to check that d is a metric on x, usually referred to as the discrete metric. The phenomenon of concentration of measure on high dimensional structures is usually stated in terms of a metric space with a borel measure, also called an mmspace. Some properties and applications of fuzzy quasipseudo. Introduction a quasimetric space is a set x equipped with a quasimetric d, i. Submittedto topology proceedings quasimetric spaces. Fixedpoint theorem for multivalued quasicontraction maps. Ciric, a generalization of banachs contraction principle, proc amer.
A minimization theorem in quasimetric spaces and its. Best proximity point theorems in partially ordered bquasi. Metric space, contraction mapping, fixed point theorem, quasi metric space, pconvergent, porbit ally continuous. The basic example of such an action is when k is compact, g. Completions a notcomplete metric space presents the di culty that cauchy sequences may fail to converge. As applications, some previous results are obtained from these theorems as special cases. A characterization of smyth complete quasimetric spaces. Manifolds dusek, zdenek and kowalski, oldrich, 2007. Generalized the result of hitzler and seda in dislocated quasimetric spaces and the concept of dislocated quasimetric space is initiated by zeyada et al. This paper contains a study of families of quasipseudometrics the concept of a quasipseudometric was introduced by wilson 22, albert 1 and kelly 9 generated by proba.