Application of common fixed point theorem on fuzzy metric space. The condition of h chainable fuzzy metric are characterized to get common fixed points. In this paper we prove a fixed point theorem for six self mappings by using compatibility of type. The aim of this paper is to prove new common fixed point theorems on intuitionistic fuzzy metric spaces. As a result many authors have extended the banachs contraction principle to fuzzy metric spaces and proved fixed point and common fixed point theorems for fuzzy metric spaces. Pdf many authors have proved fixed point theorem in fuzzy probabilistic metric spaces. In this paper, we introduce the concept of fuzzy mappings in hausdorff fuzzymetric spaces in the sense of george and veeramani fuzzy sets syst. Some fixed point theorems in menger probabilistic metriclike spaces. Common fixed point theorems for owc maps in symmetric fuzzy metric spaces. The results that are presented are related to the fixed point in the fuzzy metric space. In particular, any multiemetric space is an e0metric space. In this paper are given some features and important results in the fuzzy metric space.
We also furnish an illustrative example to demonstrate the validity of the hypotheses and degree of generality of our main result. Vasuki 16 proved fixed point theorems for rweakly commutating mappings. Rhoades b e, contractive definitions and continuity, contemporary math. The notion of fuzzy metric spaces has very important applications in quantum particle physics. Coupled fixed point theorems for a pair of weakly compatible maps along withclrgproperty in fuzzy metric spaces by manish jain, kenan tas, sanjay kumar and neetu gupta get pdf 2 mb. Fixed point theorem on fuzzy metric space iopscience. Fixed point theorems in fuzzy metric spaces using implicit.
In this work, by using the new concept of hausdorff g metric in the space of fuzzy sets, we establish some common fixed point theorems for a family of fuzzy selfmappings in the space of fuzzy sets on a complete g metric space. Abstractin this paper, common fixed point theorems for fuzzy maps in fuzzy metric spaces are proved. The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of ciric in the fuzzy metric spaces. Product of fuzzy metric spaces and fixed point theorems. Pant v, discontinuity and fixed points in fuzzy metric space, j. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. The theorems which are elaborated provide the existence and uniqueness of the fixed point in the complete fuzzy metric space. Fixed point theorems for geraghty contraction type. Fuzzy sets and systems 46 1992 1071 107 northholland on fixed point theorems in fuzzy metric spaces jinxuan fang department of mathematics, nanjing normal university, nanjing, jiangsu 210024, china received december 1989 revised april 1990 abstract. Common fixed point theorems for six self mappings in fuzzy. Fixed point theorems in mfuzzy metric space techrepublic.
Pdf this paper is an attempt to prove some critically analysed results on the fixed point theorems, which are unique. Some common fixed point theorems in fuzzy metric spaces. We prove a related fixed point theorem for four mappings which are not continuous in four fuzzy metric spaces, one of them is a sequentially compact fuzzy metric space. Common fixed point theorems for fuzzy mappings in bmetric space 421 a fuzzy set in x is a function with domain x and values in 0. This paper offers the fixed point theorems on fuzzy metric spaces, which generalize, extend and fuzzify several known fixed point theorems for compatible maps on metric space, by making use of implicit relations. Pdf fixed point theorem in fuzzy metric spaces researchgate. In this paper we obtain a common fixed point theorem for six self maps on fuzzy metric space by using implicit relation.
Common fixed point theorems on fuzzy metric spaces using. We give fixed point theorems for complete fuzzy metric spaces in the sense of george and veeramani, and also for kramosil and michaleks fuzzy metric spaces which are complete in grabiecs sense. Journal of applied mathematics and physics, 6, 228231. Some fixed point theorems of ciric type in fuzzy metric spaces. Unified fixed point theorems via common limit range property in modified intuitionistic fuzzy metric spaces common fixed point theorem in partially ordered fuzzy metric spaces fixed point theory and applications, dec 2010. Journal of inequalities and applications fuzzy fixed point theorems in hausdorff fuzzy metric spaces supak phiangsungnoen wutiphol sintunavarat poom kumam in this paper, we introduce the concept of fuzzy mappings in hausdorff fuzzy metric spaces in the sense of george and veeramani fuzzy sets syst. These theorems are fuzzy version of some known results in ordinary metric spaces. In this article, we utilize the notions of the property e. In the setting of fuzzy ultrametric spaces, we study common xed point theorems of multivalued maps.
Chouhan communicated by ayman badawi msc 2010 classi. Fuzzy fixed point theorems in hausdorff fuzzy metric. On fixedpoint theorems in fuzzy metric spaces sciencedirect. Application of common fixed point theorem on fuzzy metric. Saini, fixed point theorems and its applications in. A fixed point theorems in lfuzzy quasimetric spaces 1,2r ezasdti n1. Pdf some fixed point theorems in fuzzy bipolar metric spaces. The concept of fuzzy metric spaces has become the area of interest for researcher due to its vast applicability such as to. Some common fixed point theorems in fuzzy metric spaces by using clrg 6331 then lim. The existence of fixed points of fuzzy mappings has been an active area of research interest since heilpern introduced the concept of fuzzy mappings in 1981. Common fixed point theorems in intuitionistic fuzzy metric.
If e r, then the pseudoemetric is called a pseudometric and the pseudoe metric space is called a pseudometric space. Afterwards, beg and abbas, vasuki, popa, and imad et al. Some applications for nonlinear integral equations are also given. Jungck and rhoades 5 two self mappings f and g of a fuzzy metric space x,m. Our results generalize and extend many known results in metric spaces to a nonarchimedean fuzzy metric space in the in the sense of george and veeramani george a, veeramani p, on some results in fuzzy metric spaces.
Sapena fuzzy sets and systems 125 2002 245252 using notion of altering distance which was initiated by khan et al. Many authors 4, 7 have proved fixed point theorems in fuzzy metric space. Recently sedghi and shobe 12 introduced d metric space as a probable modification of the definition of d metric introduced by dhage 1, and prove some basic properties in d. Common fixed point theorems in modified intuitionistic. In the present paper we introduce generalized contraction mapping in fuzzy metric space and some fixedpoint theorems for gcomplete fuzzy metric space are proved.
Sharma s, common fixed point theorems in fuzzy metric spaces, fuzzy sets and systems, 1272002, 345. The aim of this paper is to obtain fixed point of mapping satisfying an implicit relation on fuzzy metric spaces. On compactness and fixed point theorems in partial metric. Fixed point theory in fuzzy metric spaces has been developed starting with the work of heilpern 11. We prove some common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces both in the sense of kramosil and michalek and in the sense of george and veeramani by using the new property and give some examples. In this paper, we introduce the concept of chainable intuitionistic fuzzy metric space akin to the notion of chainable fuzzy metric space introduced by cho, and jung 1 and prove a common fixed point theorem for weakly compatible mappings in this newly defined space. Let be a complete bounded fuzzy metric space, and a self map of satisfying for all, i then, has a unique fixed point in, and is continuous at. Following grabiecs work, fang 4 further established some new fixed point theorems for contractive type mappings in g complete fuzzy metric spaces. Some fixed point theorems on intuitionistic fuzzy metric. Fuzzy metric spaces, fuzzy 3 metric spaces, common fixed point.
He introduced the concept of fuzzy mappings and proved some. Many results have appeared related to fixed points for fuzzy mappings in. In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Fixedpoint theorems in gcomplete fuzzy metric spaces. In recent years, many authors have proved fixed point and common fixed point theorems in fuzzy metric spaces. Some fixed point theorems on intuitionistic fuzzy metric spaces with implicit relation. If a is a fuzzy set and x 2 x, then the function value ax is called the grade of membership of x in a. Fuzzy metric spaces and fixed point theorems virendra singh chouhan, v. Fixed point theorems in fuzzy metric spaces hindawi. Common fixed point theorems for fuzzy mappings in g.
Compatibility, rweakly commuting, reciprocal continuity, compatible of type. The purpose of this paper is to give some new fixed point theorems for contractive type mappings in fuzzy metric spaces. We prove a fixed point theorem for mappings satisfying an implicit relation in a complete fuzzy metric space. Branciari 1 obtained a fixed point theorem for a single mapping satisfying an analogue of banachs. At first we considered the lfuzzy metric space notation which is useful in modeling some. Common fixed point theorems in complete fuzzy metric. Our main result claims that in these spaces compactness is equivalent to sequential compactness. Unified fixed point theorems for mappings in fuzzy metric.
Many authors proved a number of common fixed point theorems by using implicit relations in different settings see 2527, 17. Our results improve and generalize the main results of mihet in mihet, 2010 and many fixed point theorems in fuzzy metric spaces. Common fixed point theorem in partially ordered fuzzy. Fixed point theorems in generalized contraction mappings. Pdf common fixed point theorems in fuzzy metric spaces. In 2008, altun and turkoglu 4 proved two common fixed point theorems for continuous compatible mappings of type and on complete. Finally, we give a fuzzy version of theorem 3 of 1. Fixed point theorem for fuzzy mappings in generalized r. In this paper, we generalize fuzzy banach contraction theorem established by v. We also show that hausdorff compact partial metric spaces are metrizable. Further, we generalize and extend some common fixed point theorems due to ali and imdad and some fixed point theorems due to mihet to the case of fuzzy metric. The researcher obtained the fuzzy version of common fixed point theorem for using extra conditions. Fixed point theorem in fuzzy metric spaces using altering. Pdf on jan 1, 2014, dhananjay gopal and others published some new fixed point theorems in fuzzy metric spaces find, read and cite all the research you need on researchgate.
A fixed point theorems in lfuzzy quasimetric spaces. Common fixed point theorems for sequences of mappings in fuzzy metric spaces khaled abdrabou department of mathematics, faculty of science, zagazig university, egypt. Many researchers have obtained common fixed point theorems for mappings satisfying different types of commutativity conditions. Common fixed point theorems for sequences of mappings in. Common fixed points, fuzzy metric space, weak compatible maps, compatible maps of type. The proof of which is done by using cauchy sequence. In the other case, there must exists some o f such that y. First, motivated by recent results, more general contractive conditions in fuzzy metric spaces are achieved and secondly, quasicontractive type. Abstract this paper introduces the notion of common fixed point theorem for three mappings in fuzzy metric space for various applications on 2 and 3metric spaces with examples. On fixed point theorems in fuzzy metric spaces sciencedirect. On fixed point theorems in fuzzy 2 metric spaces and fuzzy 3.
Fixed point theorems fixed point theorems concern maps f of a set x into itself that, under certain conditions, admit a. Our theorem in the metric version generalizes theorem 4 of 1. Fixed point theorems in fuzzy metric spaces universiteti. Common fixed point theorems for owc maps in symmetric. Pdf in the present paper we are proving a common fixed point theorem for fuzzy metric spaces for weakly commuting mappings. A coupled fixed point theorem in fuzzy metric space satisfying. M s ourv p 1d epa rtm nof m h i c sd c u s, amirkabir university of technology, tehran, iran 2 is l ami c az d u nve rt y ohb, abstract. Abstract the purpose of this paper is to study common xed point theorems for six. In this paper, we give some fixed point theorems on intuitionistic fuzzy metric spaces with an implicit relation. Fixed point theorems for weakly compatible mappings in.
Various versions of fuzzy contractive conditions are studied in two directions. Department of mathematics, shaqra university, alqawwiya, k. This result was motivation for further studies in metric spaces, as well as in the probabilistic metric spaces 6, 18, 23, 25. Some fixed point theorems in probabilistic metric spaces, stability problems for stochastic. Common fixed point theorems in fuzzy metric spaces. Moreover, two examples are represented to show the compatibility of our results. Fixed point theorems for lfuzzy mappings in quasipseudo. As patterned in jungck 16, a metrical common fixed point theorem generally involves conditions on commutatively, continuity, completeness together with a suitable condition on containment. In this paper, some new results are given on fixed and common fixed points of geraghty type contractive mappings defined in bcomplete bmetric spaces. Our results extend, generalized several fixed point theorems on metric and fuzzy metric spaces.
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