Some New Theorems of Lipschitz Type Mappings in Cone Metric Spaces

In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These results improve and generalize several wellknown comparable results in the literature. Moreover, our results are supported by some examples.

Some Fixed Point Results on a Class of Contractive Mappings in Cone Metric Spaces

In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and generalize some fixed point results in metric soaces and some previous results in cone metric spaces.

Common Fixed Point Theorems in Non-normal Cone Metric Spaces with Banach Algebras

In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover,we give an example to support the main assertions.

GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES

In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.

Common Fixed Points under Contractive Conditions in Cone Metric Spaces

In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone is not necessarily normal. Our results generalize fixed point theorems of Abbas, Jungck and Stojan Radenovi in cone metric spaces.

Common Fixed Point Results for Quasi-contractions Involving Altering Distance Functions in Ordered Cone Metric Spaces

Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.

The Completeness of Cone Metric Spaces

Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.

Common Fixed Points for a Countable Family of Non-self Mappings in Cone Metric Spaces with the Convex Prop erty

A new common fixed point result for a countable family of non-self mappings defined on a closed subset of a cone metric space with the convex property is obtained, and from which, a more general result is given. Our main results improve and generalize many known common fixed point theorems.

Some Random Coincidence Point and Common Fixed Point Results in Cone Metric Spaces Over Banach Algebras

In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.

Common Fixed Points for Mappings with Quasi-Lipschitz Conditions on TVS-valued Cone Metric Spaces

A new unique common fixed point result for a pair of mappings satisfying certain quasi-Lipschitz type conditions on a topological vector space-valued cone metric space is obtained, and its particular forms and a more general form are given. Our main results generalize and improve some well-known recent results in the literature.

Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings

In this paper, some topological concepts and definitions are generalized to cone metric spaces. It is proved that every cone metric space is first countable topological space and that sequentially compact subsets axe compact. Also, we define diametrically contractive mappings and asymptotically diametrically contractive mappings on cone metric spaces to obtain some fixed point theorems by assuming that our cone is strongly minihedral.

Some Fixed Point Theorems for Expansion onto Mappings on Cone Metric Spaces

This paper presents some fixed point theorems for expansion selfmaps on complete cone metric spaces.

Fixed Point Theorems for(p, q)-Quasi-Contraction Mappings in Cone Metric Spaces

In this work, the authors introduce the concept of(p, q)-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a(p, q)-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order 2.

Points of Coincidence for Weakly Compatible Pair of Mappings in Cone Metric Spaces

In this paper, some new existence and uniqueness of points of coincidence of weakly compatible pair of mappings is obtained, which does not satisfy continuity and commutativity. The conditions are weaker than the usual conditions in cone metric spaces.

FIXED POINT RESULTS ON METRIC-TYPE SPACES

In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.

Common Fixed Points for a Countable Family of Quasi-Contractive Mappings on a Cone Metric Space with the Convex Structure

In this paper, we consider a countable family of surjective mappings {Tn}n∈N satisfying certain quasi-contractive conditions. We also construct a convergent sequence { Xn } n c∈Nby the quasi-contractive conditions of { Tn } n ∈N and the boundary condition of a given complete and closed subset of a cone metric space X with convex structure, and then prove that the unique limit x＂ of {xn}n∈N is the unique common fixed point of {Tn}n∈N. Finally, we will give more generalized common fixed point theorem for mappings {Ti,j}i,j∈N. The main theorems in this paper generalize and improve many known common fixed point theorems for a finite or countable family of mappings with quasi-contractive conditions.

Generalized Kannan-type contraction and fixed point theorems

In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to completeness of X or normality of the cone.The continuity of the mapping is relaxed.Furthermore,we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X.These results greatly generalize several well-known comparable results in the literature.

Strong T-Stability of Picard Iteration in a Non-Normal Cone Metric Space

Let(X,d)be a cone metric space and T:X!X be a mapping.In this paper,we shall introduce the concept of strong T-stability of fixed point iteration procedures with respect to T in cone metric spaces.Also,we will investigate some meaningful results on strong T-stability of Picard iterations in cone metric spaces without the assumption of normality.Our main results improve and generalize some related results in the literature.

A Class of Ruin Probability Model with Dependent Structure

Fixed point and common fixed point results for mappings satisfying quasicontractive conditions expressed in the terms of c-distance on TVS-valued cone metric spaces（without the underlying cone which is not normal） are obtained, and P-property and Q-property for mappings in the terms of c-distance are discussed. Our results generalize and improve many known results.