Cone B-metric Spaces Research Articles

Perov type T-contractive mappings on cone b-metric spaces with generalized c-distance

The aim of this paper is to study the sufficient conditions for the existence of fixed points of Perov type T-contractive mappings in the setup of complete cone b-metric space associated with generalized c-distance. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and generalize various well known results in the existing literature.

Common Fixed Point Results Related to Generalized F-Contractions in Extended Cone b-Metric Spaces

This paper presents a new class of F-functions defined on a cone and proves some theorems showing the uniqueness and existence of common fixed points for two functions satisfying a generalized F nonlinear contractions condition in extended cone b-metric spaces. Several examples illustrate the main theorems and demonstrate the applicable side of theoretical results.

The nonlinear contraction in probabilistic cone b-metric spaces with application to integral equation

The probabilistic cone b-metric space is a novel concept that we describe in this study along with some of its fundamental topological properties and instances. We also established the fixed point theorem for the probabilistic nonlinear Banach contraction mapping on this kind of spaces. Many prior findings in the literature are generalized and unified by our findings. In order to illustrate the basic theorem in ordinary cone b-metric spaces, some related findings are also provided with an application to integral equation.

A new fixed point theorem in cone b-metric spaces

A new fixed point theorem in cone b-metric spaces

Common fixed point theorems for (φ,F)-contraction mappings in cone b-metric spaces over Banach algebra with application

Common fixed point theorems for (φ,F)-contraction mappings in cone b-metric spaces over Banach algebra with application

Fixed point result for a couple of mappings and its application via simulation in TVS-valued cone b-metric space

Fixed point result for a couple of mappings and its application via simulation in TVS-valued cone b-metric space

Fixed point result for a couple of mappings and its application via simulation in TVS-valued cone b-metric space

Fixed point result for a couple of mappings and its application via simulation in TVS-valued cone b-metric space

Some Fixed Point Results of (α,β,φ,δ) Contractions in Extended Cone b-Metric Spaces

This paper investigates the existence and uniqueness of fixed points for a class of generalized contractive mappings defined on extended cone metric spaces. Subsequently, we define and explore (α, β, φ, δ)-contractions, a generalization of traditional contractions that allows for a more nuanced understanding of the contraction behavior in extended cone metric spaces. The extended metric space was defined for the first time in 2017, by Kamran et al. (2017). They replaced the constant in the triangle inequality of the metric with a two-variable function and explored various fixed point theorems. In 2022, Das and Bag[4] introduced extended cone metric spaces by incorporating a three-variable map into the third condition of the cone metric. Afterwards, Selko and Sila introduced the concept of extended quasi cone b-metric spaces and demonstrated the Banach contraction within this framework. In 2018, Alqahtani. (2018) and colleagues established several fixed point results for a pair of orbital cyclic functions in an extended metric space. In this paper we prove some fixed point theorems for -orbital-cyclic functions in extended cone metric spaces by using the continuous map φ and a nonnegative constant δ.

Common Fixed Point Theorem for (\(\phi\),\(\mathfrak{F}\))–Multi-Valued Mappings in Cone b-Metric Spaces over Banach Algebra

In the present paper, we introduced the concept of generalized multi-valued contraction mappings, via the class functions \(\Phi\) and \(\Psi\) Also we proved some fixed point results for (\(\phi\),\(\mathfrak{F}\))- multi-valued mappings on cone b-metric spaces over Banach algebra \(\mathfrak{V}\). The conditions for existence and uniqueness of the fixed point are investigated. We give an example to support our main result.

Fixed Point Theorem for (\(\Phi\), \(\mathfrak{F}\))– Expansive Mappings in Cone b-Metric Spaces over Banach Algebra

The class functions and are used in this paper to establish the notion of fixed point theorem on expansive mappings. The primary result is a generalization of the fixed point theorem for (\(\Phi\), \(\mathfrak{F}\)) expansive mappings on cone -metric spaces over Banach algebra \(\mathfrak{V}\). Investigated are the fixed point's criteria for existence and uniqueness. Additionally, provide an illustration.

Fixed Points and Continuity Conditions of Generalized b -Quasicontractions

In this research, we first check that the abstract cone b -metric is discontinuous in the case of normal cone by a counter example. We obtain several meaningful results about generalized b -quasicontraction and Ćirić-type b -quasicontraction in cone b -metric spaces over Banach algebras, weakening certain important conditions of the spaces and the mappings. Meanwhile, several valid examples are given to demonstrate the new notions and fixed point results, when the existing theorems in the literature are not applicable.

Common new fixed point results on b-cone Banach spaces over Banach algebras

Recently Zhu and Zhai studied the concepts of cone b-norm and cone b-Banach space as generalizations of cone b-metric spaces and theygave a definition of ϕ-operator and obtained some new fixed point theorems in cone b-Banach spaces over Banach algebras by usingϕ-operator. In this paper we propose a notion of quasi-cone over Banach algebras, then by utilizing some new conditions andfollowing their work with introducing two mappings $\mathcal{T}$ and $\mathcal{S}$ we improve the fixed point theorems to the commonfixed point theorems. An example is given to illustrate the usability of the obtained results.

Fixed Point Result on Generalized Cone b-Metric Spaces

The purpose of this paper is to prove a fixed point result on contraction mapping in generalized cone b-metric space (in short GCbMS) as a generalization of cone metric space, cone b metric space and rectangular metric space. The conception of generalized metric space is a generalization of that of classical metric space. Several authors have proved fixed point theorems of contractive mappings on generalized metric spaces, which also generalized some corresponding fixed point results in classical metric spaces. In present paper, we prove a result that is extension of the Kannan fixed point theorem proved by Reny George <i>et al</i>. Our result is extend and unify several well known results in the literature available for cone and cone-b metric space.

Fixed points of mappings on extended cone b-metric space over real Banach algebra

In this article, we introduce a new geometrical structure which is the hybrid of cone metric space over Banach algebra and extended b-metric space. We prove analogues of Banach, Kannan and Reich type fixed point theorems in our introduced space. We also furnish with various concrete examples to establish the validity of our results. The obtained results generalize many well-known results in literature, especially the main results due to Vujakovic et al., Hussain et al., Huang, Radenovic, Xu become special cases of our results.

Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b -Metric Spaces over Banach Algebras

In this paper, we firstly introduce the generalized Reich‐Ćirić‐Rus-type and Kannan-type contractions in cone b -metric spaces over Banach algebras and then obtain some fixed point theorems satisfying these generalized contractive conditions, without appealing to the compactness of X . Secondly, we prove the existence and uniqueness results for fixed points of asymptotically regular mappings with generalized Lipschitz constants. The continuity of the mappings is deleted or relaxed. At last, we prove that the completeness of cone b -metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X . Our results greatly extend several important results in the literature. Moreover, we present some nontrivial examples to support the new concepts and our fixed point theorems.

Fixed point results of generalized Reich contraction for α-admissible mappings on generalized c-distance in cone b-metric spaces over Banach algebra

In this work, we introduce the nations of generalized Banach type contraction, generalized Kannan type contraction and generalized Reich type contraction for α-admissible mappings on generalized c-distance in cone b-metric spaces over Banach algebra. Then, we study the Reich fixed point results, Banach fixed point results and Kannan fixed point results for these type of mappings on generalized c-distance in such spaces. The results obtained extend and generalize several well-known results in literature. We present an example to support our work.

New common fixed point results for single-valued mappings in cone b-metric spaces over Banach algebra with generalized c-distance

In this work, we obtain common fixed point and fixed point theorems in cone b-metric spaces over Banach algebra with generalized c-distance. The presented theorems extend and generalize several well-known comparable results in literature to generalized c-distance in such space. We present an example to support our extension and generalization theorems.

Common Fixed Points of Two Mappings regarding a Generalizedc-Distance over a Banach Algebra

In this article, applying the concept of a generalizedc-distance in coneb-metric spaces over Banach algebra with a nonnormal solid cone therein, we establish several common fixed point theorems for two noncontinuous mappings satisfying the Han-Xu-type contraction. Our results are interesting, since they are not equivalent to former well-known results regarding awt-distance inb-metric spaces while they contain recent results corresponding to a generalizedc-distance in coneb-metric spaces.

Fixed point results of generalized Reich contraction for α-admissible mappings on generalized c-distance in cone b-metric spaces over Banach algebra

In this work, we introduce the nations of generalized Banach type contraction, generalized Kannan type contraction and generalized Reich type contraction for α-admissible mappings on generalized c-distance in cone b-metric spaces over Banach algebra. Then, we study the Reich fixed point results, Banach fixed point results and Kannan fixed point results for these type of mappings on generalized c-distance in such spaces. The results obtained extend and generalize several well-known results in literature. We present an example to support our work.

New common fixed point results for single-valued mappings in cone b-metric spaces over Banach algebra with generalized c-distance

In this work, we obtain common fixed point and fixed point theorems in cone b-metric spaces over Banach algebra with generalized c-distance. The presented theorems extend and generalize several well-known comparable results in literature to generalized c-distance in such space. We present an example to support our extension and generalization theorems.