The starting point was a recent result of rus and s. In this paper, we establish common fixed point theorems for two weakly compatible selfmappings satisfying the contractive condition or the quasicontractive condition in the case of a quasicontractive constant in cone bmetric spaces without the normal cone, where the coefficient s satisfies. Fixed point and common fixed point theorems on ordered cone metric spaces. Some equivalences between cone metric spaces and metric. Caccioppoli type fixed point result in cone b metric space. A fixed point theorem for bmetric space 49 caseiii. After carefully defining convergence and completeness in cone metric spaces, the authors proved some fixed point theorems of contractive mappings. We now show that results on common multipled fixed points and of course common coupled fixed points for single maps, pairs of maps and four maps in cone metric spaces can be derived from known results e. Remarks on cone metric spaces and fixed point theorems of.
Some fixed point theorems in multiplicative cone bmetric. Lectures on some fixed point theorems of functional analysis. A new concept of the cdistance in cone metric space has been introduced recently in 2011. Extended rectangular bmetric spaces and some fixed point theorems for contractive mappings zead mustafa 1.
The prototype of theorems in this class is the brouwer fixed point theorem, which states that a xed point exists provided. In this paper, we introduce a generalisation of the banach contraction mapping for fixed point theorem in complete metric space. Fixed point theorems of singlevalued mapping for c. A similar notion was also considered by rzepecki in. Then the function h has a unique fixed point remark 2. The results presented in this paper substantially improve and extend the result due to dutta and choudhary we. Pdf some fixed point theorems in d cone metric spaces. The aim of this paper is to establish a common fixed point theorem for a pair of weakly compatible mappings in a cone metric space without exploiting the notion of the continuity and we also proved a fixed point theorem in cone rectangular metric space by using rational type contraction mapping. Common fixed point theorems for two weakly compatible self. Extended rectangular metric spaces and some fixed point. Rakoceviccommon fixed points for maps on cone metric space. Caccioppoli type fixed point result in cone b metric space rima maitra department of mathematics, west bengal state university barasat, 24 paraganas north, west bengal kolkata 700126, india abstract caccioppolis fixed point result is extended to the setting of cone bmetric spaces and thus the existing result is generalized. In any d cone metric space, limits of dconvergent sequences are unique.
In the present paper, we will show common fixed point theorems for two weakly compatible selfmappings satisfying the contractive condition or quasicontractive condition in the case of a quasicontractive constant mathml in cone b metric spaces without the assumption of normality. Some fixed point theorems for multivalued contraction mappings are proved, as well as a theorem on the behaviour of fixed points as the mappings vary. In this paper we prove some xed point theorems for di erent type of contractions in the setting of a b metric space. Cone metric spaces, cone rectangular metric spaces and. Some fixed point theorems of integral type contraction in. Fixed point theorems of contractive mappings in cone bmetric. Next, by using these results, some new fixed point theorems on generalized complete algebraic cone metric spaces are proved and an example is given. Fixed point theory as an important branch of nonlinear functional analysis theory has been applied in many disciplines, see for instance 68. A generalization of bmetric space and some fixed point theorems. Pdf fixed point theorems under cdistance in ordered. Fixed point theorems for generalized quasicontractions in cone b. Fixed point theorems for multivalued mappings in cone metric spaces. Fixed point theorems for multivalued mappings in cone.
Josephs college, tiruchirappalli, tamil nadu 620 002 india. Fixed point theorems on soft metric spaces article pdf available in journal of fixed point theory and applications 192. We also prove some fixed point existence results for multivalued mappings defined on such spaces. Many fixed point theorems on bmetric spaces were stated in the literature. 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 bmetric spaces. Cho and bae presented the result of for multivalued mappings in cone metric spaces with normal cone. 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. Note that, in general a bmetric is not a continuous functional and thus so is an extended bmetric. Pdf fixed point theorems in cone metric spaces by altering. The concept of cone metric spaces over banach algebras was previously introduced by liu and xu in. Pdf multivalued fixed point theorems in cone bmetric spaces. Remarks on partial bmetric spaces and fixed point theorems nguyen van dung and vo thi le hang abstract.
In order to show this, we make use of the concept of product cone metric spaces. In this section we presented some fixed point results in cone bmetric space by using integral type contractive mappings. Some fixed point theorems in bmetric space pankaj kumar mishra, shweta sachdeva, s. Cone metric spaces and fixed point theorems of contractive. It asserts that if is a nonempty convex closed subset of a hausdorff topological vector space and is a continuous mapping of into itself such that is contained in a compact subset of, then has a fixed point. Fixed point theorems on multi valued mappings in bmetric. Common fixed point theorems in cone metric spaces article pdf available in journal of nonlinear science and applications 24. In this paper, the author first introduces the concept of generalized algebraic cone metric spaces and some elementary results concerning generalized algebraic cone metric spaces. The aim of this paper is to establish some fixed point and common fixed point theorems on ordered cone bmetric spaces. Common fixed point theorems for cyclic contractive. In this paper, we introduce the concept of partial cone bmetric spaces as a generalization of partial metric, cone metric and bmetric spaces and establish some topological properties of partial cone bmetric spaces.
Cone cclass function with common fixed point theorems for cone bmetric space r. In recent investigations, the fixed point in nonconvex analysis, especially in an ordered normed space, occupies a prominent place in many. A fixed point theorem for setvalued quasicontractions in bmetric spaces. A fixed point theorem for setvalued quasicontractions in.
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. Then, xn is a cauchy sequence if and only if dxn,xm. Stonetype theorem on bmetric spaces and applications. A generalised common fixed point theorem of taskovic type for three mappings f. By replacing the real numbers with an ordered banach space, huang and zhang 1 defined cone metric spaces and proved some fixed point theorems of contractions on cone metric spaces. On nadlers fixed point theorem for partial metric spaces. Multivalued fixed point theorems in cone bmetric spaces. As applications, we show that xed point theorems on partial bmetric spaces can be implied from certain xed point theorems on bmetric spaces. Coincidence points and common fixed points for expansive type. The aim of this paper is to extend and generalize some fixed point theorems on cdistance in cone metric space 1. The existence of a common fixed point on cone metric space was. Pdf fixed point theorem in complete metric space top.
Fixed point theorems in b metric spaces with applications. Cone metric spaces and fixed point theorems of contractive mappings. An extended bmetric space x,dq is complete if every cauchy sequence in x is convergent. Xu, fixed point theorems of contractive mappings in cone bmetric spaces and applications, fixed point theory and applications, vol.
Cone cclass function with common fixed point theorems. We also establish some fixed point theorems for selfmappings defined on such spaces. On generalized algebraic cone metric spaces and fixed. Dhamodharan 2 1department of mathematics,urumu dhanalakshmi college tiruchirappalli620019, india email. Some generalized results of fixed points in cone bmetric spaces. The presented theorems extend, generalize and unify several recent results in the literature. In this paper we study on contribution of fixed point theorem in metric spaces and quasi metric spaces. The concept of cone metric spaces is a generalization of metric spaces, where each pair of points is assigned to a member of a real banach space with a cone, for new. If suppose that then taking, we get, therefore is the fixed point of t. Fixed point and common fixed point theorems on ordered. The main theorem extends several well known comparable results in the existing literature. D be a d cone metric space and suppose that the sequence fx ngin xis dconverge to xand z.
Theorems 14 generalize the fixed point theorems of contractive mappings in metric spaces to cone metric spaces. In addition, by using our results, we obtain the existence and uniqueness of solution to some ordinary differential equations with initial value. Banach contraction principle and kannans fixed point theorem is proved in this space. In this paper we prove some xed point theorems for di erent type of contractions in the setting of a bmetric space. Fixed point theorems on multi valued mappings in bmetric spaces j. Throughout this paper, we firstly offer some new examples in cone bmetric spaces, then obtain some fixed point theorems of contractive. The schauder fixed point theorem is an extension of the brouwer fixed point theorem to topological vector spaces, which may be of infinite dimension. Rezapour and hamlbarani presented the results of for the case of a cone metric space without normality in cone. Multipled fixed point theorems in cone metric spaces. In this paper, we introduce the concept of algebra cone generalized bmetric space over banach algebra by replacing the constant s. Algebra cone generalized bmetric space over banach. They proved some fixed point theorems of generalized lipschitz mappings with weaker conditions on the generalized lipschitz constant k by means of the spectral radius see theorems 2. Triangle inequality comparison function unique fixed point quasimetric space. Varga, on ekelands variational principle in bmetric spaces.
An application of our main result is also provided. In this paper we establish some topological properties of the cone bmetric spaces and then improve some recent results about kkm mappings in the setting of a cone bmetric space. Fixed point theorems of contractive mappings in cone b. Recently, hussain and shah16 introduced the concept of cone bmetric spaces. Remarks on partial bmetric spaces and fixed point theorems. A generalization of bmetric space and some fixed point. Algebraic cone metric spaces and fixed point theorems of. In this paper, we introduces the notion of multiplicative cone bmetric space and prove some. We verify the tstability of picards iteration and the p property for such mappings. Common fixed point theorems for mappings satisfying ea. The proposed theorems expand and generalize several wellknown comparable results in the literature to ordered cone bmetric spaces. In the present work, some fixed point and common fixed point theorems for selfmaps on ordered cone metric spaces, where the cone is not necessarily normal, are proved. Pdf in this paper we establish some fixed point theorems by altering distances in a complete cone.
D cone metric space and fixed point theorem 211 theorem 2. Our results extendgeneralize many preexisting results in literature. In this paper, we prove some properties of a partial bmetric space in the sense of shukla. Fixed point theorems under cdistance in ordered cone metric space.
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