Mappings In Cone Metric Spaces Research Articles

Results in Cone Metric Spaces and Related Fixed Point Theorems for Contractive Type Mappings

The purpose of this article, is to establish some fixed point results for contractive type mappings in cone metric spaces. Examples are provided to support results and concepts presented herein. As an application of our results, we deduce other established fixed point theorems in cone metric spaces.

Almost Contraction Mappings and $(S,T)$-Stability of Jungck Iteration in Cone Metric Spaces over Banach Algebras

In this work, we first introduce almost contraction mappings for a pair of two mappings in cone metric spaces over Banach algebras (CMSBA). Then, we observe that the class of such mappings in this setting contains those of many well known mappings. Finally, we prove some fixed point theorems, and obtain $(S,T)$-stability results of Jungck iterations for some mappings in CMSBA.

Fixed Point of Contractive Mappings in Cone Metric Space

The concept of a fixed point of a function is closely related to the abstract space of the function it is in, one of which is the cone metric space which is a generalization of the metric space and which was first introduced by Zhang and Huang in 2007. The cone metric space is any non-empty set that with cone metric function. The cone metric function has the domain of any non-empty set and has the codomain of an ordered Banach space. The purpose of this study is to recognize the concept of the cone metric space and its relation to the metric space, as well as to examine the fixed point theorem on the cone metric space.

Caristi’s Fixed Point Theorem in Cone Metric Space

In this paper, we provide a short, comprehensive, and brief proof for Caristi-Kirk fixed point result for single and set-valued mappings in cone metric spaces. In addition, we partially addressed an open problem in which Caristi-Kirk fixed point result in cone metric spaces reduces to a classical result in metric spaces and provided a brief justification for a partial positive answer to this open problem using Caristi-Kirk fixed point theorem on uniform space. The proofs given to Caristi-Kirk’s result vary and use different techniques.

Fixed point theorems under Rhoades and Reich contractive conditions in complete cone metric spaces

One of the extended metric space concepts is a cone metric space. The cone metric space was first proposed by Guang and Xian in 2007. In their research, they introduced Banach fixed point theorems in complete cone metric space, namely by analogizing the fixed point theorems in complete metric space. They add normal properties to the cone set. However, Rezapour in 2008 refuted Banach fixed point theorems in cone metric space by eliminating normal properties of the cone set. For this reason, we will investigate the existence and uniqueness of Rhoades and Reich contractive mappings in cone metric space by referring to the research of Guang and Rezapour.

Almost contraction mappings in cone $b$-metric spaces over Banach algebras

We introduce the condition of being Cauchy for a sequence in cone $b$-metric spaces (cbms) over Banach algebras. Based on this result, we extend almost mappings in cone metric spaces over Banach algebras to cbms over Banach algebras and prove the related fixed point theorem. In addition, we apply our results to some applications to illustrate their usability.

Common Fixed Point theorem in Cone Metric Spaces Over Banach Algebras

In this paper, a common fixed point theorem for four mappings in cone metric spaces over Banach algebras is proved without assuming the normality of underlying cone. The results of this paper unify, generalize and extend some known results in cone metric spaces over Banach algebras. An example is presented which shows the significance of the result proved herein.

Convergence of the Ishikawa Type Iteration Process with Errors of I-Asymptotically Quasi-nonexpansive Mappings in Cone Metric Spaces

The goal of this article is to consider an Ishikawa type iteration process with errors to approximate the fixed point of -asymptotically quasi non-expansive mapping in convex cone metric spaces. Our results extend and generalize many known results from complete generalized convex metric spaces to cone metric spaces.

Fixed point Theorems of Multivalued Mappings in Cone Metric Spaces via Cone C-Class function

Fixed point Theorems of Multivalued Mappings in Cone Metric Spaces via Cone C-Class function

Some Fixed Point Theorems on Generalized Contractive mappings in cone metric space

Some Fixed Point Theorems on Generalized Contractive mappings in cone metric space

English

English

English

English

Coupled fixed point theorem and t-stability for nonlinear contractive mappings in cone metric spaces over Banach algebras

In this paper, we establish the existence of coupled coincidence point and prove coincidence point theorem for nonlinear contractive mappings in cone metric space over Banach algebras. Our results generalize some known results in cone metric space. Moreover, we verify the T-stability of iteration sequence.

Some Remarks on Perov Type Mappings in Cone Metric Spaces

Let \(\left( E,C,t\right) \) be a real ordered topological vector space and let (X, d) be a tvs-cone metric space over cone C. Using Proposition 19.9 of Deimling (Nonlinear functional analysis, Springer, Berlin, 1985), we show that E can be equipped with a norm such that C is a normal monotone solid cone. Hence, a tvs-cone metric space \(\left( X,d\right) \) over a solid cone C is a normal cone metric space over the same cone C. This assures that tvs-cone metric spaces are not a genuine generalization of cone metric spaces introduced by Huang and Zhang, recently. Further, if the cone C is solid then we have only cone metric spaces over normal solid cone (with coefficient of normality \(K=1\)). Here, we introduce also the notion of Sehgal–Guseman–Perov type mappings and we establish a result of existence and uniqueness of fixed points for this class of mappings.

Coincidence Points and Common Fixed Points for Four Self-Mappings via Weakly Compatible Mappings in Cone Metric Spaces

In this paper, we obtain coincidence points and common fixed point theorem for four self-mappings via weakly compatible mappings in cone metric spaces, where the cone is not necessarily normal. These results are improved and generalized several well- known comparable results existing in the references.

On Common Fixed Point Results for Set-Valued Mappings in Cone Metric Spaces

On Common Fixed Point Results for Set-Valued Mappings in Cone Metric Spaces

Some Fixed Point Theorems for Expansive Mappings in Cone Pentagonal Metric Spaces

In this paper, we prove some xed point theorems for mappings satisfying expansive conditions in non-normal cone pentagonal metric spaces. Our results extend and improve the recent results announced by Patil and Salunke [Fixed point theorems for Expansion mappings in Cone rectangular metric spaces, Gen. Math. Notes, 29(1), (2015), 30-39], Shatanawi and Awawdeh, [Some xed and coincidence point theorems for Expansive maps in Cone metric spaces, Fixed Point Theory and Applications, 1(2012), 1-10], Huang, Zhu and Wen, [Fixed point theorems for Expanding mappings in Cone metric spaces, Math. Reports 14(64), 2(2012), 141-148], Kadelburg, Murthy and Radenovic, [Common xed points for Expansive mappings in Cone metric spaces, Int. J. Math. Anal, 5(27), (2011), 1309-1319], Aage and Salunke, [Some xed point theorems for Expansion onto mappings on Cone metric spaces, Acta Mathematica Sinica, 27(6), (2011), 1101-1106], Kumar and Garg, [Common xed points for Expansion mappings Theorems in metric spaces, Int. J. Contemp. Math. Sciences, 4(36), (2009), 1749-1758], and many others in the literature.

Common Caristi-type Fixed Point Theorem for Two Single Valued Mappings in Cone Metric Spaces

Common Caristi-type Fixed Point Theorem for Two Single Valued Mappings in Cone Metric Spaces

Fixed points of Perov type contractive mappings on the set endowed with a graphic structure

The aim of this paper is to present fixed point results of Perov type contractive mappings in the framework of cone metric spaces endowed with a graphic structure. Some examples are presented to support the results proved herein. We also provide an example to show that our results are substantial generalization of comparable results in the existing literature. As an application of our results, we obtain fixed point results of Perov type cyclic contraction mappings in cone metric spaces.

A note on generalized operator quasicontractions in Cone Metric Spaces

In a recent paper [Fixed point theorem for generalized operator quasi-contractive mappings in cone metric spaces, Afrika Mat., DOI 10.1007/ s13370-012-0105-7], X. Zhang has used bounded positive definite linear operators on the given Banach space in an attempt to obtain a more general fixed point result in a normal cone metric space. We will show in this paper that most of the conditions in his theorem are superfluous and that the proof can be obtained in amuch easier way, by reducing it to a well known Ćirić's result on quasicontractions in standard metric spaces.