Fixed point theorems in generalized contraction mappings in. 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. Common fixed point theorems for fuzzy mappings in bmetric space. In this case, we obtain an ordered version of boyd and wongs xed point theorem in complete metric spaces equipped with a partial order as follows. Some common fixed point theorems in fuzzy metric spaces by. Common fixed point theorems for a pair of weakly compatible. Diagonal lemma, also known as the fixedpoint lemma, for producing selfreferential sentences of firstorder logic. 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. Aug 04, 2015 fixed point theorems in gcomplete fuzzy metric spaces. Fixedpoint combinator, which shows that every term in untyped lambda calculus has a fixed point.
Suzuki type theorems in triangular and nonarchimedean. Motivated by the concepts of fuzzy metric and m metric spaces, we introduced the notion of non archimedean fuzzy m metric space which is an extension of partial fuzzy metric space. The weak compatibility of a and s implies that asu sau and then. The aim of this article is to utilize the no tion of the property e. Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces wutiphol sintunavarat and poom kumam department of mathematics, faculty of science, king mongkuts university of technology thonburi kmutt, bangmod, bangkok 10140, thailand correspondence should be addressed to poom kumam, poom.
Common fixed point theorem for weakly compatible mappings in intuitionistic fuzzy metric spaces anju panwar, department of mathematics, maharshi dayanand university, rohtak, haryana 124001, india abstract the present paper deals with a common fixed point theorem for weakly compatible mappings using condition of integral type in. Pdf fixed point theorems in strong fuzzy metric spaces. Some fixed point theorems in gmetric and fuzzy metric spaces. Sintunavarat 20 introduced a new concept of property clrg. 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. Common fixed point theorems for sequences of mappings in fuzzy metric spaces khaled abdrabou department of mathematics, faculty of science, zagazig university, egypt. Issn published by world academic press, world academic union 17467659, england, uk journal of information and computing science vol. 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. Common fixed point theorems in fuzzy metric spaces employing. In this paper, inspired by the concept of b metric space, we introduce the concept of extended b metric space. We prove a common fixed point theorem for mappings under contractive conditions in fuzzy metric spaces.
Fuzzy metric spaces and fixed point theorems 209 which is a contradiction. Salunke 3establised some results on fixed point theorem in fuzzy metric space. The purpose of this paper is to find some commonfixed point theorems for occasionally weakly compatible mapping 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. Fixed point theorems in fuzzy mathematics has got a direction of vigorous hope and vital trust with the study of kramosil and michalek10, who introduced the concept of fuzzy metric space. In these three areas, the boundary lines can be detected by employing the theorems such as 1 brouwers fixed point theorem 2 banach s fixed point theorem 3 tarski s fixed point theorem. The main objective of this paper is to obtain some fixed point theorems in the setting of fuzzy metric spaces using weak compatibility, semi. On fixedpoint theorems in fuzzy metric spaces sciencedirect. It follows f and g satisfy clrg property then we can find a sequence x n. Our results generalize or improve many recent fixed point theorems in the literature. In this paper, they mainly prove a coincidence theorem and common fixed point theorem in for generalized m fuzzy 2 metric space which improves the results of fixed point theorems. Tripled fixed point theorem in fuzzy metric spaces and. If e r, then the pseudoemetric is called a pseudometric and the pseudoe. In 1967, goguen 1 introduced the notion of fuzzy sets as a generalization of fuzzy sets 2.
In 1981, heilpern 3 first introduced the fuzzy of x for each. 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. The aim of this paper is to prove new common fixed point theorems on intuitionistic fuzzy metric spaces. Pdf fixed point theorems and its applications in fuzzy. Sep 19, 2012 kaewcharoen and kaewkhao and tahat et al. Fixed point theorems in intuitionistics fuzzy metric. In this paper, we state and prove some common fixed point theorems in fuzzy metric spaces. Common fixed point, fuzzy 2 metric spaces, weakly compatible introduction the concept of fuzzy sets was introduced initially by zadeh 1965. A fuzzy metric space x, m, t is complete if every cauchy sequence is convergent. The aim of this paper is to introduce and study certain new concepts of proximal contractions in an intuitionistic fuzzy metric space. Regarding this notion, its topological structure and some properties are specified simultaneously.
Nonarchimedean fuzzy mmetric space and fixed point. Gupta and mani 21, 24 proved some fixed point theorems in fuzzy metric spaces through rational inequality. Multivalued caristis type mappings in 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.
As an application, we deduce best proximity and fixed point results in partially ordered intuitionistic 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. In some earlier work, watson and rhoades 22, 23 proved several fixed point theorems involving a very general contractive definition. Fuzzy metric spaces and fixed point theorems virendra singh chouhan, v. Fixed points of fuzzy mappings in ordered metric spaces. In this paper, we establish a common fixed point theorem for fuzzy maps satisfying nonexpansive type condition on complete linear metric space. 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 in intuitionistic fuzzy metric. Common fixed point theorems for sequences of mappings in. Some common fixed point theorems in fuzzy metric spaces by using clrg property. A common fixed point theorem in complete fuzzy metric spaces. Common fixed point theorems for fuzzy mappings in g metric.
Fixed points in fuzzy metric spaces, fuzzy sets and systems, vol. Naser abbasi, hamid mottaghi golshan, mahmood shakori. Common fixed point theorem for weakly compatible mappings in. Department of mathematics, shaqra university, alqawwiya, k.
Fixed point and periodic point theorems in fuzzy metric space. Under the assumptions of corollary 5, we have, by virtue remark 3, that sequence tx, converges to the unique fixed point of i. Moreover, we present some examples to illustrate and support our results. Pdf fixed point theorem in fuzzy metric spaces researchgate. These theorems generalize and improve known results see. The purpose of this paper is to introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some new fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces. Pdf some fixed point theorems in fuzzy metric spaces. 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. Abstract this paper introduces the notion of common fixed point theorem for three mappings in fuzzy metric space for various applications on 2 and 3 metric spaces with examples. General terms fuzzy metric spaces, fixed point theory keywords.
Jun 12, 20 issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. On some new fixed point results in fuzzy b metric spaces. In this paper we prove an existence and uniqueness theorem for contractive type mappings in fuzzy metric spaces. Fixed point theorems in generalized contraction mappings. As application of the abovementioned concept, we will establish some tupled fixed point theorems for contractive type mappings in fuzzy metric space which. 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. Further we establish fixed point theorems for such kind of mappings in nonarchimedean and triangular fuzzy metric spaces. Later on, this concept of fuzzy metric space was modified by george and veeramani4. The presented theorems extend, generalize and improve the corresponding results given in the literature. Some common fixed point theorems in fuzzy metric spaces using. The concept of compatibility in fuzzy metric space and proved some common fixed point theorems in fuzzy metric space in the sense of george and veeramani with continuous t norm defined by a b.
Fixed point theorems in fuzzy metric spaces using clrg property. Bag department of mathematics, visvabharati west bengal, india email. Our results generalize several known results in the literature. Fuzzy fixed point theorems in hausdorff fuzzy metric spaces.
Many authors 4, 7 have proved fixed point theorems in fuzzy metric space. A to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces. Caristis fixed point theorem is one of the most useful among these generalizations, which further has been extended and generalized by many authors in several. Common fixed point theorems on fuzzy metric 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. Some common fixed point theorems in fuzzy metric spaces by using clrg 6333 for all x,y. Common fixed point theorems on fuzzy metric spaces using implicit relation sunny chauhan 1 and neeraj dhiman 2 1near nehru training centre, h. Next, we obtain xed point theorems in rectangular quasi metric spaces. Also, a common fixed point theorem for sequence of. In fixed point theory, implicit relations are employed to embrace several contractive conditions at a stroke instead of proving a separate theorem for each contraction.
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 2 metric spaces and fuzzy 3. In this paper we present some common fixed point theorems for occasionally weakly compatible mapping in fuzzy metric spaces. Sharma and deshpandey 30 proved common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces.
We prove the theory of integral type contraction as an application. For more details about fuzzy metric spaces and fixed point theorems in these spaces, among a huge number of the papers regarding this topic, we suggest for reading the papers 5, 8, 19, 21, 22, 2527, 30. Kumar, bhatia and manro 10 proved common fixed point theorems for weakly maps sa. Cho and jung 2 proved a common fixed point theorem for four weak compatible mappings of an chainable fuzzy metric space. Our results extendgeneralize many preexisting results in literature. Common coupled fixed point theorems for contractive mappings. The topology being hausdorff, a sequence can converge at most to one point.
Fixed point theorems in mfuzzy metric space techrepublic. In the present chapter we will find some fixed point theorems in random fuzzy metric space, random fuzzy 2 metric space and random fuzzy 3 metric space through rational expressionmotivated by 17 and 8. We also establish common fixed point theorems for a family of fuzzy selfmappings in the space of fuzzy sets on a complete gmetric space. Turkoglu 9 gerenelized junkck common fixed point theorem to intuitionistic fuzzy metric spaces. We present some examples in support of this new notion. Sapena fuzzy sets and systems 125 2002 245252 using notion of altering distance which was initiated by khan et al.
Fixed point theorem in intuitionistic fuzzy metric spaces. In this paper, we generalize fuzzy banach contraction theorem established by v. Our results improve and generalize the main results of mihet in mihet, 2010 and many fixed point theorems in fuzzy metric spaces. Afterward, heilpern 3 gave the concept of fuzzy mappings and proved fixed point theorems for fuzzy contractive mappings in metric linear spaces as a generalization of nadler 4 contraction principle.
Ijmms some fixed point theorems in metric and 2 metric spaces we introduce the notion of compatibility for a pair of selfmaps on a 2 metric space and we have fixed point theorems for pairs as well as quadruples of selfmaps on a 2 metric space satisfying certain. Pdf in this paper we establish some results on fixed point theorems in strong fuzzy metric spaces by using control function, which are the. In 1992, matthews 17 introduced a concept, and basic properties of. Then we establish certain best proximity point theorems for such proximal contractions in intuitionistic fuzzy metric spaces. If f and g satisfy clrg property then f and g have a unique common fixed point. Common fixed point theorems on fuzzy metric spaces using. While proving our results, we utilize the idea of compatibility due to jungck int j math. Common fixed points, fuzzy metric space, weak compatible maps, compatible maps of type. A fuzzy metric space is said to be complete fuzzy metric space if every cauchy sequence converses in it. Some new fixed point theorems in fuzzy metric spaces. Chouhan communicated by ayman badawi msc 2010 classi. Department of mathematics, lorestan university, khoramabad, iran. Some more results of fixed point theorem in fuzzy metric spaces can be found in 12.
Common fixed point theorems in fuzzy metric spaces. The aim of this paper is to obtain fixed point of mapping satisfying an implicit relation on fuzzy 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. We offered a generalization of contraction in fuzzy metric space.
Fixed point theorems with implicit relations in fuzzy. 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. Mappings in intuitionistic fuzzy metric spaces anju panwar, department of mathematics, maharshi dayanand university, rohtak, haryana 124001, india abstract the present paper deals with a common fixed point theorem for weakly compatible mappings using condition of integral type in an intuitionistic fuzzy metric space. 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. We prove common fixed point theorem in fuzzy metric spaces in the sense of george and veeramani. A generalization of bmetric space and some fixed point. We also establish some fixed point theorems for selfmappings defined on such spaces. Pdf some new fixed point theorems in fuzzy metric spaces. Additionally, we obtain some fixed point theorems for metric spaces. Some common fixed point theorems for fuzzy maps under. The rectangular quasimetric space and common fixed point. The concept of compatibility in fuzzy metric space is introduced by singh and chauhan 4 and also proved some common.
Common fixed point theorems for fuzzy mappings in g. At the end, some fixed point results are also provided. Some common fixed point theorems in fuzzy metric spaces. Let t and f be self maps of on a fbounded fuzzy metric space x. Fixed point theorem for fuzzy mappings in generalized r. Some fixed point theorems in complete fuzzy 2 metric spaces. In particular, any multiemetric space is an e0metric space. Jain15 proved a common fixed point theorem for semicompatible mappings in fuzzy metric space using implicit relation. Jain 16 introduced the notion of semicompatible mappings in fuzzy metric space and compared this notion with the notion of compatible map of type. 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. Application of common fixed point theorem on fuzzy metric space. Some fixed point theorems in metric and 2metric spaces. Fixed points of terminating mappings in partial metric spaces. Fixed point theorems in fuzzy metric spaces using implicit.
We extend result of sharma and bamboria for fuzzy 2 metric spaces. On fixed point theorems in fuzzy 2 metric spaces and. Fuzzy fixed point theorems in hausdorff fuzzy metric. Common fixed point theorem for weakly compatible maps in. An application of fixed point theorems in fuzzy metric space.
The definitions and terminologies for further discussions are taken from heilpern. Our result generalize earlier results due to vasuki 18, chugh and kumar 3 and others. Pdf the purpose of this paper is to prove some new common fixed point theorems in gvfuzzy metric spaces. In this work, we extend and improve rectangular metric spaces to rectangular quasi metric spaces by using the concept of quasi metric spaces. The aim of this paper is to prove some common fixed point theorems for a pair of weakly compatible mappings in kromosil and michalek and. Application of common fixed point theorem on fuzzy metric. Fixed point theorems in fuzzy metric spaces sciencedirect. Abstract the purpose of this paper is to study common xed point theorems for six.
In this paper we used the concept of compatible of type p in fuzzy metric spaces. Common fixed point theorems for compatible and subsequentially. The main objective of this paper is to obtain some fixed point theorems in the setting of fuzzy metric spaces using weak compatibility, semicompatibility and an implicit relation without considering. Fixedpoint theorems in gcomplete fuzzy metric spaces. In order to do that, we consider a slight modification of the concept of a tripled fixed point introduced by berinde et al.
For examples and elementary properties of fuzzy metric spaces, we refer to 25. On fixed point theorem and applications in fuzzy metric spaces. Furthermore, spaces and mappings are very important when studying. In this paper, first we introduce certain new classes of suzuki type contractions in triangular and nonarchimedean fuzzy metric spaces. Afterwards, beg and abbas, vasuki, popa, and imad et al. The purpose of this paper is to prove some new common fixed point theorems in gv fuzzy metric spaces. The result is a genuine generalization of the corresponding result of s. In addition to fuzzy metric spaces, there are still many extensions of metric and metric space terms. Common fixed point theorems in modified intuitionistic. In, pant intorudced the new concept reciprocally continuous mappings and proved some common.
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