Cyclic Contraction Mappings Research Articles

Fixed point approaches for cyclic contraction mappings in C∗-algebra-valued b-metric spaces

Fixed point approaches for cyclic contraction mappings in C∗-algebra-valued b-metric spaces

Weakly Reich Type Cyclic Contraction Mapping Principle

Weakly Reich Type Cyclic Contraction Mapping Principle

On Cyclic Contractive Mappings of Kannan and Chatterjea Type in Generalized Metric Spaces

Novel cyclic contractions of the Kannan and Chatterjea type are presented in this study. With the aid of these brand-new contractions, new results for the existence and uniqueness of fixed points in the setting of complete generalized metric space have been established. Importantly, the results are generalizations and extensions of fixed point theorems by Chatterjea and Kannan and their cyclical expansions that are found in the literature. Additionally, several of the existing results on fixed points in generalized metric space will be generalized by the results presented in this work. Interestingly, the findings have a variety of applications in engineering and sciences. Examples have been given at the end to show the reliability of the demonstrated results.

Quadruple Best Proximity Points with Applications to Functional and Integral Equations

This manuscript is devoted to obtaining a quadruple best proximity point for a cyclic contraction mapping in the setting of ordinary metric spaces. The validity of the theoretical results is also discussed in uniformly convex Banach spaces. Furthermore, some examples are given to strengthen our study. Also, under suitable conditions, some quadruple fixed point results are presented. Finally, as applications, the existence and uniqueness of a solution to a system of functional and integral equations are obtained to promote our paper.

A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations

In the current paper, we first introduce a new class of contractions via a new notion called p-cyclic contraction mapping by combining the ideas of cyclic contraction mapping and p-contraction mapping. Then, we give a new definition of a cyclically 0-complete pair to weaken the completeness condition on the partial metric spaces. Following that, we prove some best proximity point results for p-cyclic contraction mappings on D∪E where D,E is a cyclically 0-complete pair in the setting of partial metric spaces. Hence, we generalize and unify famous and well-known results in the literature of metric fixed point theory. Additionally, we present some nontrivial examples to compare our results with earlier. Finally, we investigate the sufficient conditions for the existence of a solution to nonlinear Fredholm integral equations by the results in the paper.

Best Proximity Points of Multivalued Hardy‐Roger’s Type (Cyclic) Contractive Mappings of b‐Metric Spaces

In this article, we introduce a new type of generalized multivalued Hardy and Roger’s type proximal contractive and proximal cyclic contractive mappings of b‐metric spaces and develop some results for the existence of best proximity point(s). Moreover, we obtain some results for the existence and uniqueness of best proximity points for single‐valued mappings. Examples are given to explain the main results.

Generalized enriched cyclic contractions with application to generalized iterated function system

The purpose of this article is to initiate a new class of cyclic contraction mappings and establish a related fixed point theorem in the framework of a Banach space. To approximate the fixed point, a convergence theorem employing the Krasnoselskij iteration is presented for which a priori and a posterior error estimates are also determined. These results modify and extend several comparable results in the existing literature. As an application, we investigate the iterated function system (IFS) comprised of generalized cyclic contraction mappings. Some examples are also presented to validate the results.

Multiplicative Cyclic Contraction Mappings Class and Best Proximity Point Theorems

Multiplicative Cyclic Contraction Mappings Class and Best Proximity Point Theorems

Best Proximity Point Results for Contractive and Cyclic Contractive Type Mappings

The essential importance of the best proximity point theory is that “best proximity point theory” appears in the coincidence of “metric fixed point theory” and “optimization theory.” So finding best proximity points of mappings satisfying different type of contractive conditions in different structures is one of the fascinating research topics. For this, in this article, we first introduce a new type of proximal property of a pair of subsets of a metric space, which we designate as proximal weakly compact pair. After this, we come up with some new type of proximal contractive and proximal cyclic contractive mappings. Then we investigate the existence of best proximity point(s) in these newly originated mappings in the setting of proximal weakly compact pair of subsets in a metric space.

Some results on Best proximity in geodesic spaces

Eldred and Veeramani have proved the existence and uniqueness of best proximity for contraction cyclic contraction mapping in uniformly convex banach spaces. In this paper, Eldred and Veeramani study is extended to geodesic spaces particularly in CAT(0) spaces, prove the sequences (x_2n) and (x_2n+1) are Cauchy sequences and prove the existenace and uniqueness of best proximity point for contraction cyclic mapping in CAT(0) spaces.

Some Best Proximity Point Results for \(\mathcal{MT}\)-Rational Cyclic Contractions in \(S\)-Metric Space

In this paper, we use the concept of \(\mathcal{MT}\)-function to establish the best proximity point results for a certain class of proximal cyclic contractive mappings in \(S\)-metric spaces. Our results extend and improve some known results in the literature. We give an example to analyze and support our main results.

Coupled fixed point analysis in fuzzy cone metric spaces with an application to nonlinear integral equations

In this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.

Multivalued weak cyclic \u03b4-contraction mappings

In this paper, we propose some new type of weak cyclic multivalued contraction mappings by generalizing the cyclic contraction using the δ-distance function. Several novel fixed point results are deduced for such class of weak cyclic multivalued mappings in the framework of metric spaces. Also, we construct some examples to validate the usability of the results. Various existing results of the literature are generalized.

Existence and convergence of best proximity points in $$\mathrm{{CAT}}_\mathrm{{p}}(0)$$ spaces

In this work, we study existence and convergence of best proximity points of a cyclic contraction mapping in a complete $$\mathrm{{CAT}}_\mathrm{{p}}(0)$$ metric space, with $$p \ge 2$$. The case of coupled best proximity points of a pair of cyclic contraction mappings is also discussed. As an application, we provide sufficient conditions to obtain an extension of the Banach Contraction Principle for coupled fixed points.

Multiplicative Cyclic Contraction Mappings Class and Best Proximity Point Theorems

Multiplicative Cyclic Contraction Mappings Class and Best Proximity Point Theorems

On existence of fixed points for generalized Geraghty type almost cyclic contractions in b-metric spaces

In this paper, we estalibsh the existence and uniqueness of fixed point for generalized Geraghty type of almost cyclic contraction mappings in b-metric spaces. These results extend and generalize well-known results in [2], [4], [6], [7].

Edelstein’s Theorem for Cyclic Contractive Mappings in Strictly Convex Banach Spaces

In the current paper, we discuss sufficient and necessary conditions for the existence of best proximity points for cyclic f- contractive mappings in the setting of strictly convex Banach spaces. Extensions of Edelstein’s theorem are considered as well as an extension of a main result in Park [Park, S. (1978). Fixed points of f-contractive maps. Rocky Mountain J. Math. 8:743–750]. Another existence result of best proximity points will be obtained for asymptotically relatively nonexpansive mappings under different conditions with respect to the recent paper of Rajesh and Veeramani [Rajesh, S., Veeramani, P. (2016). Best Proximity point theorems for asymptotically relatively nonexpansive mappings. Numer. Funct. Anal. Optim. 37:80–91].

Best Proximity Points of -Cyclic Contractions with Property UC

We initiate the notion of generalized - cyclic contraction mappings with respect to an auxiliary function and investigate the existence of a best proximity point of such mappings in the setting of metric spaces. We also prove the uniqueness of a fixed point, when we assume an additional condition, named as: property UC. Moreover, we discuss the existence and uniqueness of a fixed point of -cyclic orbital contractions in the context of (b-metric) metric spaces.

Fixed point theorems for Cyclic-Ćirić-Reich-Rus contraction mapping in quasi-partial b-metric spaces

In this paper, Cirić-Reich-Rus cyclic contraction mapping is defined in the setting of quasi-partial b-metric spaces and fixed point results are proved. Some examples are given to validate our results.