Fixed point theorem, fuzzy metric spaces, contractions. 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. Grabiec, 1998 followed kramosil and michalek,1975 and obtained fuzzy version of banachs,1982 fixed point theorem. Kumam, generalized common fixed point theorems in complex valued metric spaces and. Naser abbasi, hamid mottaghi golshan, mahmood shakori. Note that this happen when we consider the fuzzy metric space in the. On the other hand, bhaskar and lakshmikantham 3, lakshmikantham and ciric 8, gave some coupled fixed point theorems in partially ordered metric spaces. Afterwards, beg and abbas, vasuki, popa, and imad et al. Application of common fixed point theorem on fuzzy metric space. The definitions and terminologies for further discussions are taken from heilpern.
Some common fixed point results for a rational inequality. The aim of this paper is to prove new common fixed point theorems on intuitionistic fuzzy metric spaces. Fixed point theorem in fuzzy metric space using clrg. We give fixedpoint 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. He introduced the concept of fuzzy mappings and proved some. Further we establish fixed point theorems for such kind of mappings in nonarchimedean and triangular fuzzy metric spaces. The purpose of this paper is to find some commonfixed point theorems for occasionally weakly compatible mapping in fuzzy metric spaces. These theorems generalize and improve known results see. Fixed point theorems in fuzzy metric spaces using clrg. Caristis fixed point theorem and its equivalences in fuzzy metric. Following the approach of gregori and sapena, in this paper we introduced a new class of contractions and we establish some common fixed point theorems in gcomplete fuzzy metric. Bag department of mathematics, visvabharati west bengal, india email. Common fixed point theorems in fuzzy metric spaces employing. While proving our results, we utilize the idea of compatibility due to jungck int j math.
For the reader convenience, we recall some terminology from the theory of fuzzy metric spaces. Common fixed point theorems in fuzzy metric space using. Some common fixed point theorems in fuzzy metric spaces. We define fuzzy contraction mapping and try to established fixed point theorem in fuzzy metric space. Edelstein, on fixed and periodic points under contractive mappings. Veeramani, on some results in fuzzy metric spaces, fuzzy sets and systems. Common fixed points, fuzzy metric space, weak compatible maps, compatible maps of type.
Fixed point theorems for lfuzzy mappings in quasipseudo. In order to do that, we consider a slight modification of the concept of a tripled fixed point introduced by berinde et al. In the present paper we introduce generalized contraction mapping in fuzzy metric space and some fixedpoint theorems for gcomplete fuzzy metric space are proved. His result is a generalization of the fixed point theorem for pointtoset maps of nadler 4. Common fixed point theorems in a new fuzzy metric space weiquan zhang,1 dong qiu,2 zhifeng li,1 and gangqiang xiong1 1 school of information engineering, guangdong medical college, dongguan, guangdong 523808, china 2 college of mathematics and physics, chongqing university of posts and telecommunications, nanan, chongqing 400065, china. Additionally, we obtain some fixed point theorems for metric spaces. 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 metric spaces. The aim of this article is to utilize the no tion of the property e. Fixed point theorems in product spaces 729 iii if 0 t. The weak compatibility of a and s implies that asu sau and then. Related fixed point theorems in fuzzy metric spaces. In this paper, we state and prove some common fixed point theorems in fuzzy metric spaces.
Our results unify, extend, and generalize some related common fixed point theorems of the literature for both ultrametric spaces wang and song 20, gajic 2002 and 2001 and fuzzy metric spaces vijayaraju and sajath 2011. We also prove suzuki type fixed point results in nonarchimedean and triangular ordered fuzzy metric spaces. Fixed point and periodic point theorems in fuzzy metric space. Pdf some common fixed point theorems using implicit. Sapena fuzzy sets and systems 125 2002 245252 using notion of altering distance which was initiated by khan et al. If e r, then the pseudoemetric is called a pseudometric and the pseudoe metric space is called a pseudometric space. Therefore, several fixed point theorems for types of fuzzy contractive mappings have appeared see, for instance 1,59. Singh and jain7 further extended the result of popa 14 15 in fuzzy metric spaces. Common fixed point theorems for sequences of mappings in fuzzy metric spaces khaled abdrabou department of mathematics, faculty of science, zagazig university, egypt. Common fixed point theorems for fuzzy mappings in bmetric space.
Common fixed point theorems of multivalued maps in fuzzy. In this paper we introduce fixed point theorems for generalized contraction mapping in. Fuzzy metric space, induced fuzzy metric space, contraction mapping in fuzzy metric space. Common fixed point theorems in fuzzy metric space with. The aim of this paper is to introduce the new definition of r fuzzy metric space and establish a fixed point theorem for fuzzy mappings in generalized r fuzzy metric spaces.
K2 is a convex, closed subset of a banach space x and t2. Department of mathematics, shaqra university, alqawwiya, k. Common fixedpoint theorems in gcomplete fuzzy metric. Also a theorem on the equivalency related to completeness is given. Pdf suzukitype fixed point theorem for fuzzy mappings. These theorems generalize and improve known results see 1. Common fixed point theorems in modified intuitionistic fuzzy.
We give some new definitions of compatible mappings of types i and ii in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible. Tripled fixed point theorem in fuzzy metric spaces and. Application of common fixed point theorem on fuzzy metric. Our results generalize and extend results of mongkolkeha et al. Fixed point theorems in fuzzy metric space under strict then by lemma 2 we have conclusion.
Fixed point theorems in fuzzy metric spaces sciencedirect. In particular, any multiemetric space is an e0metric space. In this paper, we state and prove some common fixed point. On fixed point theorems in fuzzy 2 metric spaces and. Fixed point theorems in generalized contraction mappings. Fixedpoint theorem for multivalued quasicontraction maps in a v.
Common fixed point, fuzzy metric space, semi compatible maps, weakly compatible maps, clrg property. Our results generalize several known results in the literature. In this paper we extend this concept to fuzzy metric space and establish the existence of related xed points theorems for two pairs of mappings. Pdf some new fixed point theorems in fuzzy metric spaces. Fixed point theorems in generalized contraction mappings in. It is proved that every metric space can induce a fuzzy metric space that is complete whenever, the original one is complete.
Extended fuzzy metrics and fixed point theorems mdpi. For examples and elementary properties of fuzzy metric spaces, we refer to 25. In this paper we prove an existence and uniqueness theorem for contractive type mappings in fuzzy metric spaces. Fixed point theory in fuzzy metric spaces has been developed starting with the work of heilpern 11. Fixed point theorems in fuzzy metric spaces using implicit. Fuzzy metric spaces, fuzzy 2metric spaces, intuitionistic fuzzy metric spaces, common xed point, intuitionistic fuzzy 2metric spaces. Some common fixed point theorems in fuzzy metric spaces using implicit relations mahdi azhini1 department of mathematics, science and research branch islamic azad university, tehran, iran m.
The results are a genuine generalization of the corresponding results of gregori and sapena. The result is a genuine generalization of the corresponding result of s. Kramosil and michalek 15 introduced fuzzy metric space, george and veermani 7 modified the notion of fuzzy metric spaces with the help of continuous tnorms. In the setting of fuzzy ultrametric spaces, we study common fixed point theorems of multivalued maps. 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 for a pair of weakly compatible. Common fixed point theorems on fuzzy metric spaces using implicit relation sunny chauhan 1 and neeraj dhiman 2 1near nehru training centre, h. These are the generalizations of many results in the recent literature. Fixed point theorem in fuzzy metric spaces using altering distance.
Recent literature on fixed point theory in fuzzy metric spaces may also be viewed in 5, 6, 7, 24. Fixed point theorems and its applications in fuzzy metric. Sintunavarat 20 introduced a new concept of property clrg. We prove the fuzzy analogue of the edelsten theorem in fuzzy 3 metric space. On fixed point theorems in fuzzy 2 metric spaces and fuzzy 3. Some fixed point theorems in complete fuzzy 2 metric spaces. A metric modular on a nonempty set x is a function. Common fixed point theorems for fuzzy mappings in b metric space 421 a fuzzy set in x is a function with domain x and values in 0. In this paper, we generalize fuzzy banach contraction theorem established by v. Some fixed point theorems in complete fuzzy 2 metric spaces mintu lal saha. In an earlier paper 3, the present author introduced an idea of fuzzy cone metric space and established some basic results and. The aim of the presented paper is to study the fixed point theorems in complete and compact fuzzy metric spaces as improvement of some recent results m.
Pdf some fixed point theorems in fuzzy bipolar metric spaces. Abstract the purpose of this paper is to study common xed point theorems for six. Vasuki 28 practiced the term rweakly commuting mapping in fuzzy metric spaces and proved some common fixed point theorems for these. Suzuki type theorems in triangular and nonarchimedean.
Kumam, common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, journal of applied mathematics, vol. Chauhan et al 6 utilize the notion of common limit range property to prove unified fixed point theorems for weakly compatible mapping in fuzzy metric spaces. The main objective of this paper is to obtain some fixed point theorems in the setting of fuzzy metric spaces using weak compatibility, semi. Common fixed theorem on intuitionistic fuzzy 2metric spaces. In this paper, we utilize the clrs and jclrst properties to prove some existence theorems of common fixed point for contractive mappings in fuzzy metric spaces. Common fixed point theorems on fuzzy metric spaces using. On fixed point theorems in fuzzy metric spaces 1 introduction emis. Under the assumptions of corollary 5, we have, by virtue remark 3, that sequence tx, converges to the unique fixed point of i. In 1981, heilpern 3 first introduced the fuzzy of x for each.
On fixedpoint theorems in fuzzy metric spaces sciencedirect. Common coupled fixed point theorems in intuitionistic. Common fixed point theorems on fuzzy metric spaces. The topology being hausdorff, a sequence can converge at most to one point.
Cho and jung 2 proved a common fixed point theorem for four weak compatible mappings of an chainable fuzzy metric space. Some common fixed point results for a rational inequality in. Common fixed point theorems for sequences of mappings in. The aim of this paper is to obtain fixed point of mapping satisfying an implicit relation on fuzzy metric spaces. In this paper we prove a periodic point theorem in fuzzy metric space and present some common fixed point theorems for occasionally weakly compatible mappings in fuzzy 3 metric spaces under various conditions. The purpose of this paper is to prove some new common fixed point theorems in gv fuzzy metric spaces. Common coupled fixed point theorems for contractive. The aim of this paper is to introduce the new definition of rfuzzy metric space and establish a fixed point theorem for fuzzy mappings in generalized rfuzzy metric spaces. Fixed point theorem for fuzzy mappings in generalized r. General terms fuzzy metric spaces, fixed point theory keywords. Using d metric concepts, sedghi and shobe define fuzzy metric space and proved a common fixed point theorem in it. 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.
Fixedpoint theorems in gcomplete fuzzy metric spaces. However, the study of related xed points for two pairs of mappings is also interesting. Many authors 4, 7 have proved fixed point theorems in fuzzy metric space. Original article fixed point and periodic point theorems in fuzzy metric space binod chandra tripathy1, sudipta paul2, and nanda ram das3 1 mathematical sciences division, institute of advanced study in science and technology, paschim boragoan, garchuk, guwahati, assam, 781035 india. The purpose of this paper is to prove some new common fixed point theorems in gvfuzzy metric spaces. Let t and f be self maps of on a fbounded fuzzy metric space x.
Common fixed point theorems in modified intuitionistic. 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 common fixed point theorems in fuzzy metric spaces. Jun 12, 20 issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. Common coupled fixed point theorems for contractive mappings. Common fixed point theorems in a new fuzzy metric space. In addition, we can prove fuzzy edelsteins contraction theorem. Salunke 3establised some results on fixed point theorem in fuzzy metric space. Department of mathematics, lorestan university, khoramabad, iran.
Common fixed point theorems in fuzzy metric spaces. Aug 04, 2015 fixed point theorems in gcomplete fuzzy metric spaces. We prove a common fixed point theorem for mappings under contractive conditions in fuzzy metric spaces. A to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces. Fuzzy metric spaces and fixed point theorems 209 which is a contradiction. Our results generalize several previously known results in various spaces which include results in intuitionistic fuzzy metric spaces and metric spaces. Kx x k2 k2 is a kset contraction with respect to hausdorff measure of noncompactness, then t tx, t2.