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