Pdf a generalized metric space has been defined by branciari as a metric space in which the triangle inequality is replaced by a more general. These results generalize the existing fixed point results in the. Fixed point theorems for lcontractions in generalized metric spaces. Fixed point theorems for generalized contractions in metric. In this paper, we give a survey of recent results on reducing fixed point theorems on generalized metric spaces to fixed point theorems on metric spaces and then investigate this fact in other generalized metric spaces. First we prove common fixed point theorems for weakly compatible maps which generalize the results of chen 2012. If e r, then the pseudoemetric is called a pseudometric and the pseudoe. First we prove common xed point theorems for weakly compatible maps which generalize the results of chen. Some common fixed point theorems in generalized metric spaces. Some fixed points theorems in generalized d metric.
In this paper, we state and prove some common fixed point theorems in fuzzy metric spaces. A fixed point theorems for pointwise contractive semigroup of self mappings in setting of generalized metric space are proved. Pdf a fixed point theorem in generalized metric spaces. Mathematics subject classification 2000 47h10, 54h25.
Pdf generalized common fixed point theorems in complex. Secondly, we prove common xed point theorems using property e. At the end, we prove common xed point theorems using common limit range property clr property along with weakly compatible maps. Some fixed point theorems in generalized dislocated metric spaces. Josephs college, tiruchirappalli, tamil nadu 620 002 india. In this paper, the notion of lcontractions is introduced and a new fixed point. Then aghajani, abbas and roshan studied a new type of. Common fixed point theorems in digital metric spaces. Some common fixed point theorems in complex valued metric spaces. Fixed point theorems for generalized contractions in metric spaces. The topology being hausdorff, a sequence can converge at most to one point.
Fixed point theorems for l contractions in generalized. The concept of a metric space is a very important tool in many scientific fields and partic ulary in the fixed point theory. On some fixed point theorems in generalized metric spaces. Caristis fixed point theorem and subrahmanyams fixed point theorem in. In this article, we extend and improve the condition of contraction of the results of azam et al.
The aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by jleli and samet in fixed point. In this paper, we obtain some generalizations of fixed point results for kannan, chatterjea and hardyrogers contraction mappings in a new. Pdf caristis fixed point theorem and subrahmanyams. In particular, any multiemetric space is an e0metric space. In this paper, we prove two unique common coupled fixedpoint theorems for jungck type and for three mappings in symmetric fuzzy metric spaces. In this paper, we obtain some generalizations of fixed point results for kannan, chatterjea and. Abdou, fixed point theorems for generalized contraction mappings in multiplicative metric spaces, j. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces for example. Afterwards, rezapour and hamlbarani 9 proved fixed point theorems of contractive type mappings by omitting the assumption of normality in cone metric spaces.
A fixed point theorem in generalized metric spaces. Subsequently, many authors studied the fixed point theory in the setting of complete metric spaces and obtained some fixed point theorems for different contractions see 110. Research article some common fixed point theorems in. Fixed points of a new type of contractive mappings in complete metric spaces. In this paper, we introduce a concept of the cdistance in a cone metric space and, by using the concept of the cdistance, prove some fixed point theorems in ordered cone metric spaces. An existence theorem for volterratype integral inclusion is establish in bmetric spaces. Fixed point theorems in generalized metric spaces with.
In this paper we consider, discuss, improve and generalize recent fixed point results for mappings in bmetric, rectangular metric and rectangular metric spaces established by dukic et al. Seghals result then by deriving the generalized dislocated analogues of fixed point theorems of banach. Pdf generalized probabilistic metric spaces and fixed. Common fixed point theorems in digital metric spaces ijser. Particularly, our result has as a particular case, mappings satisfying a general contractive condition of integral type. In this paper we obtain points of coincidence and common fixed points for three self mappings satisfying jungck 5 type contractive condition with. Fixed point theorems in fuzzy metric spaces sciencedirect. Sedghi, shobe and aliouche defined the notion of smetric spaces and proved some fixedpoint theorems on a complete smetric space 20.
Common coupled fixedpoint theorems in generalized fuzzy. A fixed point theorem in generalized metric spaces in. A generalized metric space and related fixed point theorems. We want to extend some well known fixed point theorems which are also valid in b metric space. Some fixed point theorems for generalized kannan type mappings. We also derive some new fixed point results in ordered partial metric spaces. Fixed point theorems for generalized weakly contractive.
In recent years, this notion has been generalized in several directions and many notions of a metric type space was introduced b metric, dislocated space, generalized metric space, quasi metric space, symmetric space, etc. On some fixed point theorems in generalized metric spaces fixed. Jul 12, 2016 the aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by jleli and samet in fixed point theory appl. Mar 12, 20 in this article, we establish some fixed point theorems for weakly contractive mappings defined in ordered metric like spaces. Fixed point theorems in generalized contraction mappings in. Fixed point theorems for weakly contractive mappings in.
These results generalize some wellknown results in the literature. Pdf in this paper, we obtain some generalizations of fixed point results for kannan, chatterjea and hardyrogers contraction mappings in a. This result includes those of jachimski equivalent conditions and the meirkeeler type theorems, j. We discuss fishers fixed point theorem for mappings defined on a generalized metric space endowed with a graph. Cone metric spaces and fixed point theorems of generalized. Pdf some fixed point theorems in extended bmetric spaces. Pdf in 1994, matthews introduced the notion of a partial metric space in order to obtain a suitable mathematical tool for program verification. Some fixed point theorems concerning fcontraction in complete metric spaces. Secondly, we prove common fixed point theorems using property e.
In such spaces, we establish new versions of some known fixed point theorems in standard metric spaces including banach contraction principle, cirics fixed point theorem, a fixed point result due to ran and reurings, and a fixed point result due to nieto and rodiguezlopez. Pdf a fixed point theorem in generalized metric space. Sehgalthomas type fixed point theorems in generalized metric. Fixed point theorems on generalized bmetric spaces 147 leteness of x, it follows that there exists x. Fixed point theorems in generalized partially ordered g metric spaces dedicated to t. Common fixed point theorems in complex valued metric spaces. In the paper we present fixed point theorems in generalized bmetric spaces both for linear and nonlinear contractions, generalizing several existing results.
We introduce a new concept of generalized metric spaces for which we extend some wellknown fixed point results including banach contraction principle, cirics fixed point theorem, a fixed point result due to ran and reurings, and a fixed point result due to nieto and rodriguezlopez. Fixed point theorems in metric spaces sciencedirect. Rational contraction in multiplicative metric spaces. Our results generalize, improve, and simplify the proof of the previous results given by some authors. Concretely, we show that the matthews fixed point theorem does not constitute, in principle, an appropriate implement for the aforementioned purpose.
A function is called a b metric provided that for all 1 if and only if, 2, 3. Our purpose is to show that some wellknown fixed point theorems are valid in metricb spaces. Department of mathematics, srm university, haryana, sonepat 1001, india. Pdf a generalization of fixed point theorems in smetric. Some common fixed point theorems in complex valued metric. This is a generalization of some well known fixed point results in. Kumam, generalized common fixed point theorems in complex valued metric spaces and applications, journal of inequalities and applications, vol. Generalized probabilistic metric spaces and fixed point theorems. Common fixed point theorems in complex valued metric spaces manoj kumar1. Nov 27, 2017 the concept of a metric space is a very important tool in many scientific fields and particulary in the fixed point theory. Pdf on some fixed point theorems in generalized metric spaces. Before giving our main results, we recall some of the basic concepts and results in metric spaces and fuzzy metric spaces. In this paper we introduce the notion of generalized d metric space and prove some fixed point theorems in complete generalized d metric spaces. In order to appreciate the idea involved in the results of fixed point theorems of monotone operators in a partially ordered metric spaces,, including this paper, several remarks are in order.
In this article, we modified and generalized a contraction mapping of azam et al. Fixed point theorems in generalized partially ordered g. If the inline pdf is not rendering correctly, you can download the pdf file here. We first introduce two new fcontractions of hardyrogers type and then establish fixed point theorems for these contractions in the setting of bmetric spaces.
Inspired by the preceding fact, we prove two fixed point theorems which provide the mathematical basis for a new technique to carry out asymptotic complexity analysis of algorithms via partial. It is interesting that we see some properties in usual metric space is not valid in bmetric space. A new kind of nonlinear quasicontractions in metric spaces. Pdf fixed point theorems in generalized metric spaces with. Pdf fixed point theorems on generalized bmetric spaces. Generalization of fixed point theorems in ordered metric. Jun, 2014 there have been many attempts to generalize the definition of a metric space in order to obtain possibilities for more general fixed point results. Various generalizations of metric spaces and fixed point. We provide an example and some applications in order to support the useability of our results. Generalized common fixed point theorems in complex valued metric spaces and applications article pdf available in journal of inequalities and applications 20121. Kumara swamy2 1department of mathematics school of advanced sciences vit university vellore, 632014, tamil nadu, india. Fixed point theorems in partially ordered metric spaces and. At the end, we prove common fixed point theorems using common limit range property clr property along with weakly compatible maps. Fixed point theorems on multi valued mappings in bmetric spaces.
Mar 10, 2011 fixed point results with the concept of generalized weakly contractive conditions in complete ordered metric spaces are derived. Some fixed points theorems in generalized d metric spaces. Fixed point theorems on multi valued mappings in bmetric spaces j. On some well known fixed point theorems in metric spaces. His result is a generalization of the fixed point theorem for point toset maps of nadler. Jumaili and yang, used the concept of a d metric space and introduced a new concept of the. We introduce the notion of generalized contraction and establish some new fixed point theorems for this contraction in the setting of complete metric spaces. We also improve caristis and subrahmanyams fixed point theorems in the space. Through the proof of the above extension, we understand more deeply the mathematical structure of a. In this paper we introduce fixed point theorems for generalized contraction mapping in fuzzy metric spaces. The latest generalized metric space is bv s metric space which is introduced by. May 23, 2014 in the present paper, we give some fixed point results for generalized ciric type strong almost contractions on partial metric spaces which generalizes some recent results appearing in the literature. Common fixed point theorems on generalized distance in.
Therefore, several fixed point theorems for types of fuzzy contractive mappings have appeared see, for instance. Fixed point theorems for generalized almost contractions in. Many problems in pure and applied mathematics reduce to a problem of common fixed point of some selfmapping operators which are defined on metric spaces. Using the basic result some consequences are derived. Fixed point theorems in new generalized metric spaces. In this paper we have obtained some fixed point theorems on b metric space which is an extension of a fixed point theorem by hardy and reich 20. A fixed point theorems for pointwise contractive semigroup of selfmappings in setting of generalized metric space are proved. One of the generalizations of metric spaces is the partial metric space in which selfdistance of points need not to be zero but the property of symmetric and modified version of triangle inequality is satisfied. Aug 11, 2011 in this article, we consider ordered metric spaces concerning generalized distance and prove some fixed point theorems in these spaces. In literature,there are several generalized metric spaces. Generalized common fixed point theorems in complex valued. Fisher fixed point results in generalized metric spaces with a graph. This new concept of generalized metric spaces recover various topological spaces including standard. Using d metric concepts, sedghi and shobe define fuzzy metric space and proved a common fixed point theorem in it.