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. On completeness in quasimetric spaces sciencedirect. 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. The aim of this paper is to investigate some fixed point results in dislocated quasi metric dqmetric spaces. Isufati 1 proved fixed point theorems for a single map and a pair of mappings in dislocated metric spaces. 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. Fixed point results in dislocated quasi metric spaces. By an example we illustrate the limits of the construction. Mathematics free fulltext modified suzukisimulation. In this paper, we introduce the concept of a setvalued or multivalued quasicontraction mapping in v fuzzy metric spaces. Fixedpoint theorem for multivalued quasicontraction maps.
A few examples of generalized metric spaces are quasi metric spaces, cone metric spaces,gmetric spaces, dislocated metric spaces,bmetric. 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. In particular, applications to two interesting examples of partial metric spaces which appear in computer science, as the domain of. 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. 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. Since quasi metric spaces form a generalization of metric spaces, any sound completion theory for such. The banach contraction principle forms the basis of metric fixed point theory.
Some of this material is contained in optional sections of the book, but i will assume none of that and start from scratch. Quasimetric spaces transition systems prevision transition systems add action labels 2l, to control system. Ciric, a generalization of banachs contraction principle, proc amer. Pdf the purpose of this work is to study topological properties of bdislocated quasimetric space and derive some fixed point theorems.
It is not hard to check that d is a metric on x, usually referred to as the discrete metric. We establish convergence theorems of a sequence in quasimetric spaces. 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. 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. Fixed point theorems for ciric type contractions in. They called a t 0quasimetric space qhyperconvex if and only if it is injective in the category of t 0. The basic example of such an action is when k is compact, g.
As applications, some previous results are obtained from these theorems as special cases. Hans triebel a new approach to function spaces on quasimetric spaces where. We show that the bicompletion of a weightable quasimetric space is a weightable quasimetric space. Quasicontractions on metric spaces 325 for all x,y in x for which the righthand side of the inequality is positive. Dhage 2 introduced the concept of d metric spaces and proved several fixed point theorems in it. We prove a new minimization theorem in quasimetric spaces, which improves the results of takahashi 1993. Some properties and applications of fuzzy quasipseudo. Xxxr is called a metric or distance function if ad only if.
Submittedto topology proceedings quasimetric spaces. In, mustafa and sims introduced the concept of a gmetric space as a generalized metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. Pdf quasi metrics have been used in several places in the literature on domain theory and the formal semantics of programming languages. This paper considers the problem of defining cauchy sequence and completeness in quasipseudometric spaces. After that, many fixed point theorems on gmetric spaces were. Some properties and applications of fuzzy quasipseudometric spaces sorin nadaban1, ioan dzitac1,2. The metric topology on a metric space m is the coarsest topology on m relative to which the metric d is a continuous map from the product of m with itself to the nonnegative real numbers. A new generalized quasi metric space with some fixed. Reasonably, we want to repair this situation, and in as economical way as possible. Introduction some convergence theorems of certain iterations to a. Pdf the geodesic problem in quasimetric spaces qinglan. Some new observations on geraghty and ciric type results in.
A new concept in dislocated and dislocated quasi metric. These questions are subsumed by computing simulation hemimetrics between 1 and. If g acts geometrically on x and y proper geodesic metric spaces then x and y are quasiisometric. Department of mathematics, university of leicester, leicester, lei 7rh. We introduce a definition of recursive quasimetric spaces in analogy to recursive metric spaces. We also demonstrate that the main results of the paper cover several existing results in the literature. We introduce a novel approach towards harnacks inequality in the context of spaces of homogeneous type. 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 axiomatic approach to harnacks inequality in doubling quasimetric spaces sapto indratno, diego maldonado, and sharad silwal abstract. We do not develop their theory in detail, and we leave the veri. 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. Further, this theorem is used to generalize caristis fixed point theorem and ekelands.
Generalized the result of hitzler and seda in dislocated quasimetric spaces and the concept of dislocated quasimetric space is initiated by zeyada et al. A characterization of smyth complete quasimetric spaces. Completions a notcomplete metric space presents the di culty that cauchy sequences may fail to converge. Dislocated quasibmetric spaces and fixed point theorems. 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.
Introduction let x be an arbitrary set, which could consist of vectors in rn, functions, sequences, matrices, etc. On completeness in quasimetric spaces introduction core. Note that iff if then so thus on the other hand, let. Fixed point results for different types of contractive conditions are established, which generalize, modify and unify some existing fixed point theorems in the literature. Cauchy sequences in quasipseudometric spaces springerlink. A notion of cauchy sequence in quasimetric spaces is introduced and used to define a standard completion for a special class of spaces. Sets of biological sequences with some commonly used similarity. Completely metrizable spaces are often called topologically complete. This study showed that fixed point theorems for two mappings in quasi jsmetric spaces were proved. Since such spaces are quasimetrizable but nonmetrizable, we will need to develop our theory in the realm of quasimetric spaces. Fixed point theorems in dislocated quasi d metric spaces. Pdf on statistical convergence in quasimetric spaces. Pdf on generalized quasi metric spaces researchgate. Pdf contribution of fixed point theorem in quasi metric.
Pdf a quasimetric is a distance function which satisfies the triangle inequality but is not symmetric in general. A minimization theorem in quasimetric spaces and its. There are many ways to make new metric spaces from old. Many authors invented the generalizations of metric spaces by various ways and established the contraction mapping theorem in it. Metric spaces are first countable since one can use balls with rational radius as a neighborhood base. A new approach to function spaces on quasimetric spaces. Mlaiki, nabil dedovic, nebojsa aydi, hassen gardasevicfilipovic, milanka binmohsin, bandar and radenovic, stojan 2019. Using this new concept, a fixedpoint theorem is established. It is clear that b metric spaces, quasib metric spaces and b metriclike spaces are dqb metric spaces but converse is not true. Quasiisometries kevin whyte berkeley fall 2007 lecture 1 theorem 1. Then the pair x,d is called dislocated quasi bmetric space or in short dqb metric space. Quasimetric tree in t0quasimetric spaces sciencedirect. 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.
Families of quasipseudometrics generated by probabilistic quasipseudometric spaces mariusz t. Best proximity point theorems in partially ordered bquasi. On the moduli spaces of leftinvariant pseudoriemannian metrics on lie groups kubo, akira, onda, kensuke, taketomi, yuichiro, and tamaru, hiroshi, hiroshima mathematical journal, 2016. We dene continuous function and prove generalized weierstrass theorem in this work. 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.
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. Bicompleting weightable quasimetric spaces and partial. Bag abstract the skeleton of this manuscript consists of a concept of compact quasimetric space and some fundamental behaviors of this space. We obtain a quasimetric generalization of caristis fixed point theorem for a kind of complete quasimetric spaces. In this paper, we prove some best proximity point theorems for ordered rational proximal contractions of. In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set. T,quasimetric space x, d has to be defined in such a manner that the following requirements are fulfilled.
Introduction a quasimetric space is a set x equipped with a quasimetric d, i. Xthe number dx,y gives us the distance between them. Finally, we acquired graphical fixed point results in nonarchimedean quasi modular metric spaces. A geometric action is a group action that is cocompact, isometric, and properly discontinuous. In this paper we study on contribution of fixed point theorem in metric spaces and quasi metric spaces. Metric space, contraction mapping, fixed point theorem, quasi metric space, pconvergent, porbit ally continuous. 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. Since the conclusion of the baire category theorem is purely topological, it applies to these spaces as well. We extend some of the mmspace concepts to the setting of a quasi.
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