We also prove suzuki type fixed point results in nonarchimedean and triangular ordered fuzzy metric spaces. K2 is a convex, closed subset of a banach space x and t2. 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 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. 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. Singh and jain7 further extended the result of popa 14 15 in fuzzy metric spaces. In this paper we introduce fixed point theorems for generalized contraction mapping in. Common fixed point theorems in modified intuitionistic fuzzy. Application of common fixed point theorem on fuzzy metric space. Vasuki 28 practiced the term rweakly commuting mapping in fuzzy metric spaces and proved some common fixed point theorems for these. On fixed point theorems in fuzzy metric spaces 1 introduction emis. Some common fixed point theorems in fuzzy metric spaces using. Salunke 3establised some results on fixed point theorem in fuzzy metric space. The results are a genuine generalization of the corresponding results of gregori and sapena.
Department of mathematics, shaqra university, alqawwiya, k. Fixed point theorems in fuzzy metric spaces sciencedirect. In order to do that, we consider a slight modification of the concept of a tripled fixed point introduced by berinde et al. Related fixed point theorems in fuzzy metric spaces. The purpose of this paper is to find some commonfixed point theorems for occasionally weakly compatible mapping in fuzzy metric spaces. The aim of this article is to utilize the no tion of the property e. The results presented here improve and generalize certain recent results from the literature. In particular, any multiemetric space is an e0metric space. Fixed point theorems in generalized contraction mappings in. Fixed point theorems and its applications in fuzzy metric. In the setting of fuzzy ultrametric spaces, we study common fixed point theorems of multivalued maps.
Tripled fixed point theorem in fuzzy metric spaces and. 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. Common fixed points, fuzzy metric space, weak compatible maps, compatible maps of type. 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. Some fixed point theorems in complete fuzzy 2 metric spaces. Fuzzy metric spaces and fixed point theorems 209 which is a contradiction.
General terms fuzzy metric spaces, fixed point theory keywords. 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. Cho and jung 2 proved a common fixed point theorem for four weak compatible mappings of an chainable fuzzy metric space. Veeramani, on some results in fuzzy metric spaces, fuzzy sets and systems. 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. A to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces.
Pdf common fixed point theorems in fuzzy metric spaces. Using d metric concepts, sedghi and shobe define fuzzy metric space and proved a common fixed point theorem in it. 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. Further we establish fixed point theorems for such kind of mappings in nonarchimedean and triangular fuzzy metric spaces. Fixed point theorems in product spaces 729 iii if 0 t. Common fixed point theorems in modified intuitionistic. 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 fixedpoint theorems in gcomplete fuzzy metric. 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. 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. Kx x k2 k2 is a kset contraction with respect to hausdorff measure of noncompactness, then t tx, t2.
Common fixed point theorems for fuzzy mappings in bmetric space. Suzuki type theorems in triangular and nonarchimedean. In this paper we prove an existence and uniqueness theorem for contractive type mappings in fuzzy metric spaces. If e r, then the pseudoemetric is called a pseudometric and the pseudoe metric space is called a pseudometric space. Fixed point theorems in generalized contraction mappings. Common fixed point theorems in fuzzy metric spaces. In 1981, heilpern 3 first introduced the fuzzy of x for each.
Aug 04, 2015 fixed point theorems in gcomplete fuzzy metric spaces. We prove the fuzzy analogue of the edelsten theorem in fuzzy 3 metric space. Application of common fixed point theorem on fuzzy metric. If e r, then the pseudoemetric is called a pseudometric and the pseudoe. Pdf suzukitype fixed point theorem for fuzzy mappings. Fixedpoint theorems in gcomplete fuzzy metric spaces. Common fixed point theorems for sequences of mappings in. Fixed point theorem in fuzzy metric space using clrg. Common fixed point theorems in fuzzy metric spaces employing. Fixed point theorem, fuzzy metric spaces, contractions.
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. The aim of this paper is to obtain fixed point of mapping satisfying an implicit relation on fuzzy metric spaces. Fuzzy metric space, induced fuzzy metric space, contraction mapping in fuzzy metric space. The purpose of this paper is to prove some new common fixed point theorems in gv fuzzy metric spaces.
The definitions and terminologies for further discussions are taken from heilpern. Jun 12, 20 issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. In the present paper we introduce generalized contraction mapping in fuzzy metric space and some fixedpoint theorems for gcomplete fuzzy metric space are proved. On fixed point theorems in fuzzy 2 metric spaces and fuzzy 3.
Common fixed point theorems on fuzzy metric spaces using implicit relation sunny chauhan 1 and neeraj dhiman 2 1near nehru training centre, h. Sintunavarat 20 introduced a new concept of property clrg. Some common fixed point theorems in fuzzy metric spaces. Our results generalize several previously known results in various spaces which include results in intuitionistic fuzzy metric spaces and metric spaces. Caristis fixed point theorem and its equivalences in fuzzy metric. In this paper, we state and prove some common fixed point theorems in fuzzy metric spaces. Fixed point theorems in fuzzy metric spaces using implicit. 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. Many authors 4, 7 have proved fixed point theorems in fuzzy metric space.
Naser abbasi, hamid mottaghi golshan, mahmood shakori. In this paper, we generalize fuzzy banach contraction theorem established by v. Grabiec, 1998 followed kramosil and michalek,1975 and obtained fuzzy version of banachs,1982 fixed point theorem. A metric modular on a nonempty set x is a function. The result is a genuine generalization of the corresponding result of s. We prove a common fixed point theorem for mappings under contractive conditions in fuzzy metric spaces. Department of mathematics, lorestan university, khoramabad, iran. Pdf some fixed point theorems in fuzzy bipolar metric spaces. Fixed point theorem for fuzzy mappings in generalized r. Pdf some common fixed point theorems using implicit. 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.
Our results generalize several known results in the literature. Some fixed point theorems in complete fuzzy 2 metric spaces mintu lal saha. Fixed point and periodic point theorems in fuzzy metric space. The purpose of this paper is to prove some new common fixed point theorems in gvfuzzy metric spaces. For examples and elementary properties of fuzzy metric spaces, we refer to 25. On fixedpoint theorems in fuzzy metric spaces sciencedirect. Sapena fuzzy sets and systems 125 2002 245252 using notion of altering distance which was initiated by khan et al. The topology being hausdorff, a sequence can converge at most to one point. Fixed point theorems in fuzzy metric space under strict then by lemma 2 we have conclusion. Common fixed point theorems in fuzzy metric space with. Under the assumptions of corollary 5, we have, by virtue remark 3, that sequence tx, converges to the unique fixed point of i. 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.
The aim of this paper is to prove new common fixed point theorems on intuitionistic fuzzy metric spaces. However, the study of related xed points for two pairs of mappings is also interesting. Kumam, common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, journal of applied mathematics, vol. Common fixed point, fuzzy metric space, semi compatible maps, weakly compatible maps, clrg property. Common fixed point theorems in fuzzy metric space using. Bag department of mathematics, visvabharati west bengal, india email. Edelstein, on fixed and periodic points under contractive mappings. Common fixed theorem on intuitionistic fuzzy 2metric spaces. 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. Our results generalize and extend results of mongkolkeha et al. 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. Kumam, generalized common fixed point theorems in complex valued metric spaces and. 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. While proving our results, we utilize the idea of compatibility due to jungck int j math.
It is proved that every metric space can induce a fuzzy metric space that is complete whenever, the original one is complete. Some common fixed point results for a rational inequality in. In an earlier paper 3, the present author introduced an idea of fuzzy cone metric space and established some basic results and. Common fixed point theorems of multivalued maps in fuzzy. Fixedpoint theorem for multivalued quasicontraction maps in a v. In this paper, we state and prove some common fixed point. In this paper, we introduce a new class of implicit function to prove common fixed point theorems in fuzzy metric space. Common coupled fixed point theorems in intuitionistic. He introduced the concept of fuzzy mappings and proved some. Pdf some new fixed point theorems in fuzzy metric spaces. In addition, we can prove fuzzy edelsteins contraction theorem. His result is a generalization of the fixed point theorem for pointtoset maps of nadler 4.
Additionally, we obtain some fixed point theorems for 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. Abstract the purpose of this paper is to study common xed point theorems for six. Some common fixed point results for a rational inequality. Note that this happen when we consider the fuzzy metric space in the. Recent literature on fixed point theory in fuzzy metric spaces may also be viewed in 5, 6, 7, 24. Fuzzy metric spaces, fuzzy 2metric spaces, intuitionistic fuzzy metric spaces, common xed point, intuitionistic fuzzy 2metric spaces. Common fixed point theorems on fuzzy metric spaces. 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. In this paper, we introduce the concept of a setvalued or multivalued quasicontraction mapping in vfuzzy metric spaces. Also a theorem on the equivalency related to completeness is given. These theorems generalize and improve known results see 1. For the reader convenience, we recall some terminology from the theory of fuzzy metric spaces.
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. The weak compatibility of a and s implies that asu sau and then. Fixed point theorem in fuzzy metric spaces using altering distance. We define fuzzy contraction mapping and try to established fixed point theorem in fuzzy metric space.
Let t and f be self maps of on a fbounded fuzzy metric space x. 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. In this paper we obtain a common fixed point theorem for six self maps on fuzzy metric space by using implicit relation. On fixed point theorems in fuzzy 2 metric spaces and. 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. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online.
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. Common fixed point theorems for a pair of weakly compatible. Fixed point theorems in fuzzy metric spaces using clrg. These theorems generalize and improve known results see. Extended fuzzy metrics and fixed point theorems mdpi. Therefore, several fixed point theorems for types of fuzzy contractive mappings have appeared see, for instance 1,59. Fixed point theorems for lfuzzy mappings in quasipseudo. Common fixed point theorems on fuzzy metric spaces using. Fixed point theory in fuzzy metric spaces has been developed starting with the work of heilpern 11. In this paper, we prove some fixed point theorems for l fuzzy mappings in left ksequentially and rightksequentially complete quasipseudo metric spaces.