Frink used a natural approach, which we call the chain approach to. Metric spaces joseph muscat2003 last revised may 2009 a revised and expanded version of these notes are now published by springer. We investigate under what conditions a corecursively enumerable set s in a computable metric space. Fixed point theorems for weakly compatible mappings in. Also, the application of fixed points is studied for the product spaces. It is known that in a computable metric space a semicomputable set s is computable if s is a continuum chainable from a to b, where a and b are computable points, or s is a circularly chainable continuum which is not chainable. Metricandtopologicalspaces university of cambridge. Pdf coupled fixed point theorems in partially ordered. Common fixed point theorems in intuitionistic fuzzy metric spaces. Let be a complete chainable fuzzy metric space and let and be the self mappings of, satisfying the following conditions. Ranadive et al, introduced the concept of absorbing mappings in metric space and proved a common fixed point theorem in this space. Also, we characterized the conditions for three self mappings of chainable generalized fuzzy metric spaces have a unique common xed point.
A metric space is a set xtogether with a metric don it, and we will use the notation x. Metric spaces are generalizations of the real line, in which some of the theorems that hold for r. Let a be a dense subset of x and let f be a uniformly continuous from a into y. Let be a partially ordered set endowed with a metric and be a given mapping. A metric space y is clocally linearly connected if there exits c. Bessem samet and habib yazidi 1 coupled fixed point theorems in partially ordered.
The rajahs college, pudukkottai 622 001, india, email. Let be a cauchy sequence in the sequence of real numbers is a cauchy sequence check it. In this paper, we introduce the notion of cchainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive. Remarks on g metric spaces and fixed point theorems. Common fixed point of semiweakly compatible maps on. The term m etric i s d erived from the word metor measur e. A of open sets is called an open cover of x if every x. Note that iff if then so thus on the other hand, let. U nofthem, the cartesian product of u with itself n times. A metric space is called complete if every cauchy sequence converges to a limit. We introduce the notion of chainable generalized fuzzy metric spaces.
Moreover, a metric space x, d is called uniformly chainable if for each. Any topological space that is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself. Xthe number dx,y gives us the distance between them. Fixed point theorems for monotone singlevalued mappings in a metric space endowed with a partial ordering have been widely investigated. Common fixed point theorems in digital metric spaces. Concerning chainability of inverse limits on 0 1 with.
An extended result on fixed point theorem in chainable. The aim of this paper is to introduce the notion of. Analysis on metric spaces summer school, lake arrowhead. Every separable metric space is isometric to a subset of the urysohn universal space. We give some conditions of which six self mappings of chainable generalized fuzzy metric space have a unique common xed point. A fuzzy metric space is called chainable if there exists an chain from to, for any. The contraction principle for mappings on a modular metric space. Chainable intuitionistic fuzzy metric space, weakly compatible maps. X a, there is a sequence x n in a which converges to x.
If v,k k is a normed vector space, then the condition du,v ku. We discuss the introduced concept of gmetric spaces and the fixed point existing results of contractive mappings defined on such spaces. Introduction the human reasoning involves the use of variable whose values are fuzzy sets. We give a generalization of the banach contraction principle on a modular metric space endowed with a graph. Any normed vector space can be made into a metric space in a natural way. Introduction let x be an arbitrary set, which could consist of vectors in rn, functions, sequences, matrices, etc. The contraction principle for mappings on a modular metric.
A rather trivial example of a metric on any set x is the discrete metric dx,y 0 if x. Jeyaraman3 1 pg and research department of mathematics, h. This paper can be seen as the modular metric version of jachymskis fixed point result for mappings. Often, if the metric dis clear from context, we will simply denote the metric space x. This allows us to use the metric don this product given by dx,y.
Let xbe a compact metric space and cx the space of continuous realvalued functions on xendowed with the supremum norm. N such that any two points in x can be joined by an. In 1922, banach 2 established a fixed point theorem known as the. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like orlicz spaces, were recently introduced. In this paper, we have introduced a new concept namely semiweakly. The topological properties of s play an important role in view of this task. For an 0, a metric space w, p is echainable if given u, vqw. We begin with an example of a metric space, and why nonzero selfdistance is worth. Fixed point theorems in fuzzy metric spaces using implicit. Since is a complete space, the sequence has a limit. An extended result on fixed point theorem in chainable fuzzy. A metric space of density equal to an infinite cardinal.
May 18, 2010 in this paper, we introduce the notion of partially ordered. A metric space x, d is called finitely chainable if for every. In this paper, we introduce the notion of partially ordered \epsilon chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces. For, distances are measured as if you had to move along a rectangular grid of8. The echainable sets with application request pdf researchgate. As a formal logical statements, this theorem can be written in the following form. Completion of a metric space a metric space need not be complete. Common fixed point theorems in intuitionistic fuzzy metric. In particular, we show that the most obtained fixed point theorems on such spaces can be deduced immediately from fixed point theorems on metric or quasimetric spaces. We introduce metric spaces and give some examples in section 1. An important example of an uncountable separable space is the real line, in which the rational numbers form a countable dense subset. Ne a metric space is a mathematical object in which the distance between two points is meaningful. A subset is called net if a metric space is called totally bounded if finite net.
If a subset of a metric space is not closed, this subset can not be sequentially compact. In this paper, we study twentyfive equivalent characterizations of finitely chainable metric spaces, out of which three are entirely new. Keywords fuzzy metric space, hchainable fuzzy metric space, compatible. These spaces were also considered in the frame of uniform spaces by hejcman in 21 who called them simply as bounded. Chainable and circularly chainable semicomputable sets in. Pdf a fixed point theorem in a generalized fuzzy metric space. We first study some properties of computable metric. Show that cx with the norm distance is a complete metric space.
We prove that this result holds in any computable topological. Keywords fuzzy metric space, h chainable fuzzy metric space, compatible. We denote by x the dual space of x and by bx the space of all. By a theorem of whyburn see 15, open maps defined on compact spaces are confluent, so an affirmative answer to this question would, of course, generalize theorem 1. Then f is continuous on x iff f 1o is an open set in x whenever o is an open set in y. We examine conditions under which, in a computable topological space, a semicomputable set is computable. Recall that every normed vector space is a metric space, with the metric dx. A chainable continuum is a metric compact connected space which admits an. Concerning chainability of inverse limits on 0 1 with set.
These theorems are hybrids of the two most fundamental and useful theorems in fixed point theory. Throughout this paper will stand for topological space. Means on chainable continua a continuum is a metric. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. Fixed point theorems for monotone singlevalued mappings in a metric space. In this paper, we introduce the notion of partially ordered. Request pdf the echainable sets with application in present.
Because every metric space has an equivalent metric that is bounded by 1, we assume throughout that all of our spaces have metrics bounded by 1. Metric spaces constitute an important class of topological spaces. Finitely chainable and totally bounded metric spaces. Using ramseys theorem a sequential characterization of uniformly chainable metric spaces is obtained, paralleling the one for totally bounded spaces. Then the printing out of each prime number is described by the chain. If all closed and bounded sets are compact, the space is called a. Then we call k k a norm and say that v,k k is a normed vector space.
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