Let be a nonempty set and thenbe a given real number. Some fixed point theorems for the maps satisfying a general contractive condition are established in this setting. Some common fixed point theorems for expanding mappings in. Fixed point theorem for multivalued functions on bmetric space. Pdf in this paper, our purpose is to show that kannan type and chatterjea type contractive mappings have unique fixed point in bmetric spaces. The intent of the paper is to introduce a g b cone metric space and study its properties.
Fixed point theorems for expansive mappings in g metric spaces. As when s 1, a b metric space is a metric space, we infer that the family of b metric spaces is larger than the one of metric spaces. 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. Cone metric spaces and fixed point theorems of contractive.
In this paper, we prove a fixed point theorem and a common fixed point theorem for multi valued mappings in complete b metric spaces. A common fixed point for six mappings in an intuitionistic mfuzzy metric space with property e 2347 abstract. Fixed point results on b metric space via picard sequences and b simulation functions marta demma a, reza saadati b. Theorems 14 generalize the fixed point theorems of contractive mappings in metric spaces to cone metric spaces. Aage and salunke 21 introduced several meaningful xed point theorems for one expanding mapping. Fixed point theorems of contractive mappings in cone b metric. In this paper, we present some fixed point theorems for a class of contractive mappings in b metric spaces. Banach contraction principle in was the starting point for many researchers during last decades in the field of nonlinear analysis. Pdf on some well known fixed point theorems in bmetric. In this section we shall prove two fixed point theorems.
Mar, 2015 very recently, malviya and fisher introduced the notion of \n\ cone metric space and proved fixed point theorems for asymptotically regular maps and sequence. Fixed point theorems on multi valued mappings in bmetric spaces j. Note that czerwik proved that the converse need not be true see also 4, 12, 18, 22 and. Afterwards, several articles which deal with fixed point theorems for singlevalued and multivalued functions in metric space appeared 18.
D be a d cone metric space and suppose that the sequence fx ngin xis dconverge to xand z. Multivalued fixed point theorems in cone bmetric spaces. Parametric metric space, parametric bmetric space and. 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. In recent investigations, the fixed point in nonconvex analysis, especially in an ordered normed space, occupies a prominent place in many. Some fixed point theorems for contractive maps in n cone. Abstract in this paper we prove some fixed point theorems for contractive as well as for expansive mappings in g metric space by using integral type contraction. Josephs college, tiruchirappalli, tamil nadu 620 002 india. We verify the tstability of picards iteration and the p property for such mappings. The results not only directly improve and generalize some fixed point results in metric spaces and b metric spaces, but also expand and complement some previous results in cone metric spaces.
Fixed point theorems of contractive mappings in cone b metric spaces andapplications. Fixed point theorems of contractive mappings in cone b. Fixed point theorems in b metric spaces with applications. A generalised common fixed point theorem of taskovic type for three mappings f. Some fixed point theorems in b metriclike spaces fixed. In other words, every metric spaces is a b metric space. The concept of a cone b metric space has been introduced recently as a generalization of a b metric space and a cone metric space in 2011. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces for example. Fixed point theorems for expansive mappings in gmetric spaces. Fixed point theorems for contractive type conditions satisfying rational inequalities in metric spaces have been developed in a number of works 9, 10, 17, 19, 20, 24. In this paper, we introduces the notion of multiplicative cone b metric space and prove some. Some common fixed point theorems in complex valued bmetric.
The aim of this paper is to establish some fixed point and common fixed point theorems on ordered cone b metric spaces. Jan 25, 2017 some fixed point theorems in b g cone metric space komal goyal1 and bhagwati prasad1,a 1 jaypee institute of information technology, department of mathematics, noida, india a corresponding author. The intent of the paper is to introduce a b g cone metric space and study its properties. We also give an example to support our main theorem. The article also includes an example which shows the validity of our result. An application of our main result is also provided. In this paper, we prove a fixed point theorem in the framework of complete partial bmetric space. In 20 the authors presented some fixed point results in cone b metric spaces without assumption of normality on cone. Some generalized results of fixed points in cone bmetric spaces. Common fixedpoint theoremsfor two selfmappingsofabmetric.
Abstract 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. In this paper, we introduces the notion of multiplicative cone bmetric space and prove some. Pdf in this paper we extend the banach contraction for multivalued mappings in a cone bmetric space without the assumption of normality on cones and. In this paper, we extended common fixed point theorem in bmetric space for two mapping using compatible mapping of type a. Fixed point theorems in partial bmetric spaces using. In 1989, bakhtin introduced the concept of b metric space as a generalization of metric spaces. In any d cone metric space, limits of dconvergent sequences are unique. A function is called a b metric provided that for all 1 if and only if, 2, 3 a pair is called a bmetric space. Pdf some fixed point theorems in extended bmetric spaces. Common fixed point theorems for mappings satisfying ea. In addition, by using our results, we obtain the existence and uniqueness of solution to some ordinary differential equations with initial value. In this paper we present some new examples in cone b metric spaces and prove some fixed point theorems of contractive mappings without the assumption of normality in cone b metric spaces.
Banerjee, some fixed point, theorems in metric b space. Our results extendgeneralize many preexisting results in literature. Since x is a complete metric space, the proof is complete. Fixed point theorems in new generalized metric spaces. We want to extend some well known fixed point theorems which are also valid in b metric space. Pdf fixed point theorems of contractive mappings in cone bmetric. A function is called a b metric provided that for all 1 if and only if, 2, 3. Generalized common fixed point theorems in complex valued. We remark that a metric space is evidently a b metric space. Also, some examples and an application to integral equation are given to support our main results. In this paper we consider, discuss, improve and generalize recent fixed point results for mappings in bmetric, rectangular metric and brectangular metric spaces established by dukic et al. In this article, we extend and improve the condition of contraction of the results of azam et al. Pdf on some well known fixed point theorems in bmetric spaces. Then x is called a sequentially compact cone metric space.
On common fixed point theorem in complete metric space. The intent of the paper is to introduce a g bcone metric space and study its properties. To begin with, we collect some definitions and basic facts on the theory of c algebras. Also we proved some fixed point results of integral type contractive mapping in cone b metric space. The pair x,d is called a b metric space with parameter s. In this paper we proved bmetric variant of xed point results for cirics and generalized contraction. Pdf in this paper we present some new examples in cone bmetric. Some fixed point theorems in multiplicative cone bmetric spaces. Fixed point results for rational type contraction in. Im looking for the proof of a theorem wich is just a generalization of nadlers results for. Common fixed point theorem in bmetric space for compatible. Bag department of mathematics, visvabharati west bengal, india email. Further, we prove some fixed point theorems in partial a bmetric space. Some fixed point theorems of integral type contraction in.
Fixed point theorems in this section we shall prove some fixed point theorems of contractive mappings. Recently, hussain and shah16 introduced the concept of cone bmetric spaces. As in the metric case, the b metric d induces a topology. This new notion generalized the notion of generalized \g\ cone metric space 4 and generalized \d\ metric space 1. If for any sequence x n in x, there is a subsequence x n i of x n such that x n i is convergent in x. Some fixed point theorems in multiplicative cone bmetric. In this paper we extend the banach contraction for multivalued mappings in a cone bmetric space without the assumption of normality on.
Distance in fuzzy cone metric spaces and common fixed point. D cone metric space and fixed point theorem 211 theorem 2. Coincidence points and common fixed points for expansive type. Some fixed point theorems in metric space endowed with graph. Czerwik see 4,5 has shown that a b metric on x need not be a metric on x.
Complete cone metric space, common fixed point, expanding mapping i introduction very recently, huang and zhang 1 introduced the. We also establish some fixed point theorems for selfmappings defined on such spaces. Later, in 1993, czerwik 15 extended the results of bmetric spaces. Fixed point theorems on multi valued mappings in bmetric spaces. Pdf multivalued fixed point theorems in cone bmetric spaces. Introduction and preliminaries fixed point theory plays one of the important roles in nonlinear analysis. In the present paper, we introduces the concept of integral type contraction with respect to cone b metric space. Fixed point theorems on multi valued mappings in bmetric. We are generalizing the well known recent results 10.
Common fixed point theorems in c algebra valued bmetric spaces. The proposed theorems expand and generalize several wellknown comparable results in the literature to ordered cone b metric spaces. Jul 21, 2015 in this work, some fixed point and common fixed point theorems are investigated in b metric like spaces. In this paper, we introduce the concept of cone b metric space over banach algebra and obtain some fixed point theorems for generalized lipschitz mappings in such settings without the assumption. In this article we present the generalized form of cho and bae 18 for the case of cone b metric spaces without normality on cone. Some of our results generalize related results in the literature. Multivalued fixed point theorems in cone b metric spaces journal. The concept of metric spaces has been generalized in many directions. Rational inequalities cannot be considered in cone metric spaces 18, but can be constructed in complex valued metric spaces. The objective was to prove some fixed point theorems for ciric type contraction in quasi js metric space which generalizes existing results in quasi js metric spaces. Banach contraction principle and kannans fixed point theorem is proved in this space. Fixed point theorems of contractive mappings in cone bmetric spaces andapplications. Fixed point and common fixed point theorems on ordered cone b.
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