Reich Contractions Research Articles

Solving Fractional Boundary Value Problems with Nonlocal Mixed Boundary Conditions Using Covariant JS-Contractions

This paper investigates the existence, uniqueness, and symmetry of solutions for Φ–Atangana–Baleanu fractional differential equations of order μ∈(1,2] under mixed nonlocal boundary conditions. This is achieved through the use of covariant and contravariant JS-contractions within a generalized framework of a sequential extended bipolar parametric metric space. As a consequence, we obtain the results on covariant and contravariant Ćirić, Chatterjea, Kannan, and Reich contractions as corollaries. Additionally, we substantiate our fixed-point findings with specific examples and derive similar results in the setting of sequential extended fuzzy bipolar metric space.

Correction to: Comments on “Fractal functions associated with Reich contractions: an approximation of chaotic attractors”

Correction to: Comments on “Fractal functions associated with Reich contractions: an approximation of chaotic attractors”

Fixed Point Theory for (μ, ψ)-Generalized Weakly Reich Contraction Mapping in Partially Ordered Metric Spaces

In this paper we introduce a concept of (μ, ψ)-generalized weakly Reich contraction mapping, and prove a fixed point theorem. Some Corollaries are consequences of the main result.

Proximity Point Results for Generalized p-Cyclic Reich Contractions: An Application to Solving Integral Equations

This article studies new classes of contractions called the p-cyclic Reich contraction and p-cyclic Reich contraction pair and develops certain best proximity point results for such contractions in the setting of partial metric spaces. Furthermore, the best proximity point results for p-proximal cyclic Reich contractions of the first and second types are also discussed.

The $(\psi,\varphi)$-Generalized Weakly Reich Contraction Mapping Theorem

In this paper we introduce a concept of $(\psi, \varphi)$-generalized weakly Reich contraction mapping and obtain a fixed point theorem. Some corollaries are consequences of the main result.

Fractal functions associated with Reich contractions: an approximation of chaotic attractors

Fractal functions associated with Reich contractions: an approximation of chaotic attractors

Reich–Krasnoselskii-type fixed point results with applications in integral equations

In this paper, motivated by Reich contraction and tool of measure of noncompactness, some generalizations of Reich, Kannan, Darbo, Sadovskii, and Krasnoselskii type fixed point results are presented by considering a pair of maps A, B on a nonempty closed subset M of a Banach space X into X. The existence of a solution to the equation Ax+Bx=x, where A is k-set contractive and B is a generalized Reich contraction, is established. As applications, it is established that the main result of this paper can be applied to learn conditions under which a solution of a nonlinear integral equation exists. Further we explain this phenomenon with the help of a practical example to approximate such solutions by using fixed point techniques. The graphs of exact and approximate solutions are also given to attract readers for further research activities.

Bi-commutative digital contraction mapping and fixed point theorem on digital image and metric spaces

The contraction mapping theorem is a powerful and most useful method in constructing the solution of linear and nonlinear systems. The principle of Banach fixed point guarantees that a self-contraction mapping of a complete metric space has a unique fixed point which can be obtain using the limit of iteration technique defined by repeated images under mapping of an arbitrary starting point in space. In this paper, we propose a Bi-commutative (II-commuting) digital maps for Kannan and Reich contraction mapping theorem and analyze the existence and uniqueness of the fixed point in the framework of digital metric spaces. We applied the contraction and commutative maps methods in proving our results. The results obtained satisfies the existence and uniqueness condition of the Banach contraction principle for a digital contraction mapping in digital metric space.

IN Mb v - COMPLETE METRIC SPACE, COMMON FIXED POINT THEOREMS FOR TWO AND FOUR SELF-MAPS UNDER DIFFERENT CONTRACTION PRINCIPLES

Two distinct theorems are presented in this manuscript. The first oneestablishes the existence of coincidence points and the g-weakness of Mbv metricspace. The Reich contraction principle produces a unique common fixed point fortwo maps, as illustrated in various examples. Second, same concept is used toidentify common fixed point for four self maps. The Kannan and Banach contractionprinciples were applied in conjunction with extra requirements to get the fixedpoints as corollaries. This theorem’s approach was used to solve several examples.

Iterative Schemes Involving Several Mutual Contractions

In this paper, we introduce the new concept of mutual Reich contraction that involves a pair of operators acting on a distance space. We chose the framework of strong b-metric spaces (generalizing the standard metric spaces) in order to add a more extended underlying structure. We provide sufficient conditions for two mutually Reich contractive maps in order to have a common fixed point. The result is extended to a family of operators of any cardinality. The dynamics of iterative discrete systems involving this type of self-maps is studied. In the case of normed spaces, we establish some relations between mutual Reich contractivity and classical contractivity for linear operators. Then, we introduce the new concept of mutual functional contractivity that generalizes the concept of classical Banach contraction, and perform a similar study to the Reich case. We also establish some relations between mutual functional contractions and Banach contractivity in the framework of quasinormed spaces and linear mappings. Lastly, we apply the obtained results to convolutional operators that had been defined by the first author acting on Bochner spaces of integrable Banach-valued curves.

A Krasnoselskii–Ishikawa Iterative Algorithm for Monotone Reich Contractions in Partially Ordered Banach Spaces with an Application

Iterative algorithms have been utilized for the computation of approximate solutions of stationary and evolutionary problems associated with differential equations. The aim of this article is to introduce concepts of monotone Reich and Chatterjea nonexpansive mappings on partially ordered Banach spaces. We describe sufficient conditions for the existence of an approximate fixed-point sequence (AFPS) and prove certain fixed-point results using the Krasnoselskii–Ishikawa iterative algorithm. Moreover, we present some interesting examples to highlight the superiority of our results. Lastly, we provide both weak and strong convergence results for such mappings and consider an application of our results to prove the existence of a solution to an initial value problem.

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.

Some remarks on contraction mappings in rectangular b-metric spaces

In this paper, we give a short proof for Reich contraction in rectangular b-metric spaces with increased range of the Lipschtzian constants and illustrate this with a suitable example. Our results generalize, improve and complement several ones in the existing literature.

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.

ϵ -Compatible Map and New Approach for Common Fixed Point Theorems in Partial Metric Space Endowed with Graph

In 2016, Muralisankar and Jeyabal introduced the concept of e-Compatible maps and studied the set of common fixed points. They generalized the Banach contraction, Kannan contraction, Reich contraction and Bianchini type contraction to obtain some common fixed point theorems for e-Compatible mappings which don't involve the suitable containment of the ranges for the given mappings in the setting of metric spaces. Motivated by this new concept of mappings, we establish a new approach for some common fixed point theorems via ϵ -compatible maps in context of complete partial metric space including a directed graph G=(V,E). By the remarkable work of Jachymski in 2008, we extend the results obtained by Muralisankar and Jeyabal in 2016. In 2008, Jachymski obtained some important fixed point results introduced by Ran and Reurings (2004) using the languages of graph theory instead of partial order and gave an interesting approach in this direction. After that, his work is considered as a reference in this domain. Sometimes, there are some mappings which do not satisfy the contractive nature on whole set M(say) but these can be made contractive on some subset of M and this can be done by including graph as shown in our Example 2.6 which is provided to substantiate the validity of our results.

New fixed point results inbv(s)-metric spaces

AbstractZ. D. Mitrović and S. Radenović introduced in [The Banach and Reich contractions inbv(s)-metric spaces, J. Fixed Point Theory Appl.19(2017), 3087–3095] a new class of generalized metric spaces and proved some fixed point theorems in this framework. The purpose of this paper is to consider other kinds of contractive mappings inbv(s)-metric spaces, and show how the work in the new settings differs from the one in standard metric andb-metric spaces. Examples show the usefulness of the obtained results.

Continuous selections and retractive representations for the fixed points sets of set valued Reich's contractions

We refine a continuous selection approach adopted earlier to fixed points of set valued Banach's contractions. An extension of selection and representation results to continuous set valued Reich's contractions is given. A new Krasnoselskii - Melvin type fixed point theorem is stated as a corollary.

Best proximity point results for Hardy\u2013Rogers p-proximal cyclic contraction in uniform spaces

The Hardy–Rogers p-proximal cyclic contraction, which includes the cyclic, Kannan, Chatterjea and Reich contractions as sub-classes, is developed in uniform spaces. The existence and uniqueness results of best proximity points for these contractions are proved. The results, which are for non-self maps, apart from the fact that they are new in literature, generalise several other similar results in literature. Examples are given to validate the results obtained.

The Banach and Reich contractions in $$\varvec{b_v(s)}$$ b v ( s ) -metric spaces

In this paper, the concept of \(b_v(s)\)-metric space is introduced as a generalization of metric space, rectangular metric space, b-metric space, rectangular b-metric space and v-generalized metric space. We next give proofs of the Banach and Reich contraction principles in \(b_v(s)\)-metric spaces. Using a new result, we provide short proofs which are different from of the original ones in metric spaces. The results we obtain generalize many known results in fixed point theory. We also provide a solution to an open problem.

On multivalued G-monotone Ciric and Reich contraction mappings

In this work, we investigate the existence of fixed points for multivalued G-monotone Ciric quasi-contraction and Reich contraction mappings in a metric space endowed with a graph G.