Geraghty Contraction Research Articles

A new fixed point approach for solutions of a $ p $-Laplacian fractional $ q $-difference boundary value problem with an integral boundary condition

<p>We explored a class of quantum calculus boundary value problems that include fractional $ q $-difference integrals. Sufficient and necessary conditions for demonstrating the existence and uniqueness of positive solutions were stated using fixed point theorems in partially ordered spaces. Moreover, the existence of a positive solution for a boundary value problem with a Riemann-Liouville fractional derivative and an integral boundary condition was examined by utilizing a novel fixed point theorem that included a $ \mathfrak{a} $-$ \eta $-Geraghty contraction. Several examples were provided to demonstrate the efficacy of the outcomes.</p>

A New Approach to the Existence of Best Proximity Points With R‐Functions in the Framework of w‐Distances

In this paper, we present a new approach to check the existence of best proximity points for R‐proximal contractions in the framework of metric spaces equipped with a w0‐distance and present elementary proofs of recent results by using the corresponding fixed point problems without the continuity assumption of the considered self‐mapping. We also discuss on cyclic Geraghty contractions and resolve the problem of the existence and convergence of the best proximity point for such a class of mappings.

Theorems of Geraghty type generalized F-contraction for dislocated quasi-metric spaces

The generalized F-contraction, Geraghty contraction and admissible function are introduced as the most recent generalizations of the Banach contraction. The presence and uniqueness of fixed points for the newly constructed contraction’s self-mapping on complete metric spaces were investigated. The findings of this article can be interpreted as an improvement on the key findings of the previous article.

On Fixed-Point Equations Involving Geraghty-Type Contractions with Solution to Integral Equation

In this study, the authors verify fixed-point results for Geraghty contractions with a restricted co-domain of the auxiliary function in the context of generalized metric structure, namely the Sb-metric space. This new idea of defining Geraghty contraction for self-operators generalizes a large number of previously published, closely related works on the presence and uniqueness of a fixed point in Sb-metric space. Also, the outcomes are achieved by removing the continuity constraint of self-operators. We also provide examples to elaborate on the obtained results and an application to the integral equation to illustrate the significance in the literature.

Fixed Points of (α, β, F*) and (α, β, F**)-Weak Geraghty Contractions with an Application

This study aims to provide some new classes of (α,β,F*)-weak Geraghty contraction and (α,β,F**)-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we find that the mappings satisfying the definition of such contractions have a unique fixed point if the underlying space is complete. In addition, we provide an application showing the uniqueness of the solution of the two-point boundary value problem.

On the construction of recurrent fractal interpolation functions using Geraghty contractions

<abstract><p>The recurrent iterated function systems (RIFS) were first introduced by Barnsley and Demko and generalized the usual iterated function systems (IFS). This new method allowed the construction of more general sets, which do not have to exhibit the strict self similarity of the IFS case and, in particular, the construction of recurrent fractal interpolation functions (RFIF). Given a data set $ \{ (x_n, y_n) \in I\times \mathbb R, n = 0, 1, \ldots, N \} $ where $ I = [x_0, x_N] $, we ensured that attractors of RIFS constructed using Geraghty contractions were graphs of some continuous functions which interpolated the given data. Our approach goes beyond the classical framework and provided a wide variety of systems for different approximations problems and, thus, gives more flexibility and applicability of the fractal interpolation method. As an application, we studied the error rates of time series related to the vaccination of COVID-19 using RFIF, and we compared them with the obtained results on the FIF.</p></abstract>

NEW FIXED POINT RESULTS FOR GERAGHTY CONTRACTIONS AND THEIR APPLICATIONS

In this paper, we prove existence and uniqueness of fixed point involving Geraghty contraction in a metric space endowed with a binary relation. Moreover, we give an application to periodic boundary value problems regarding to ordinary differential equations (ODE).

Best proximity points of multivalued Geraghty contractions

Best proximity points of multivalued Geraghty contractions

Some fixed point results for nonlinear contractive conditions in ordered proximity spaces with an application

<abstract><p>In this article, we use the concept of proximity spaces to prove common fixed point results for mappings satisfying generalized ($ \psi $, $ \beta $)-Geraghty contraction type mapping in partially ordered proximity spaces. Finally, we investigate an application to endorse our results.</p></abstract>

Survivability of AIDS Patients via Fractional Differential Equations with Fuzzy Rectangular and Fuzzy b-Rectangular Metric like Spaces

As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be regarded as the main advantage of this paper. In these spaces, the symmetry property is preserved, but the self distance may not be equal to one. We discuss topological properties and demonstrate that neither of these spaces is Hausdorff. Using α−ψ-contraction and Geraghty contractions, respectively, in our main results, we establish fixed point results in these spaces. We present examples that justify our definitions and results. We use our main results to demonstrate that the solution of a nonlinear fractional differential equation for HIV is unique.

\((\hat{\alpha}-\bar{\psi}) \text -{ Geraghty Contraction }\) on Generalized Metric Spaces with Simulation Function

In this paper, we introduce the new definitions and fixed-point theorems for \((\hat{\alpha}-\hat{\psi})\)-Geraghty contraction with an aid of simulation function \(\zeta:[0, \infty) \times[0, \infty) \rightarrow \mathbb{R}\) in generalized metric space satisfying the following condition:if \(\exists \hat{\beta} \in \mathcal{F}\) such that for all \(r, s \in \mathfrak{X}\), then we have\(\zeta[\hat{\alpha}(r, s)(d(\mathcal{P} r, \mathcal{P} \mathcal{s})), \hat{\beta}(\hat{\psi}(d(r, s))) \hat{\psi}(d(r, s))] \geq 0\), where \(\hat{\psi} \in \hat{\Psi}\) and \((\mathfrak{X}, d)\) is a generalized metric space. An example is also given to support our results.

Fixed Point of (α,β)-Admissible Generalized Geraghty F-Contraction with Application

In this paper, we introduce some new types of extended Geraghty contractions, called (α,β)-admissible generalized Geraghty F-contractions, and prove some fixed point results for such contractions in the setting of partial b-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty F-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results.

Some remarks on \u03b1-admissibility in S-metric spaces

The concept of α-admissible mapping introduced by Samet et al. (Nonlinear Anal. 75:2154–2165, 2012) has various generalizations. In this paper, we introduce the concept of alpha _{s}-admissible mapping and its various forms by generalizing the concept of α-admissible mapping in the setting of S-metric spaces. Further, we also introduce generalized rational alpha _{s}-Geraghty contraction type mappings and study the existence of fixed point theorems in S-metric spaces. Examples are also given to verify the main results.

Solving an integral equation via orthogonal generalized $ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}} $-Geraghty contractions

<abstract><p>In this paper, we introduce orthogonal generalized $ {\bf{O}} $-$ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}} $-Geraghty contractive type mappings and prove some fixed point theorems in $ {\bf{O}} $-complete $ {\bf{O}} $-$ \mathfrak{b} $-metric spaces. We also provide an illustrative example to support our theorem. The results proved here will be utilized to show the existence of a solution to an integral equation as an application.</p></abstract>

A note on three different contractions in partially ordered complex valued $ G_b $-metric spaces

<abstract><p>In this paper, we introduce the complex valued $ C^{p} $-class function, a type of Geraghty contraction and a type of JS contraction in complete partially ordered complex valued $ G_b $-metric spaces, prove three fixed point theorems in this space, and also we give some examples to support our results.</p></abstract>

On Some Coincidence Best Proximity Point Results

In this paper, we discuss some (coincidence) best proximity point results for generalized proximal contractions and λ − μ -proximal Geraghty contractions in controlled metric type spaces. To clarify our study, various examples are given and some conclusions are drawn.

Fixed point results in partially ordered partial $b_{v}(s)$-metric spaces

In this paper, some fixed point results for generalized Geraghty type $α$-admissible contractive mappings and rational type generalized Geraghty contraction mappings are given in partially ordered partial $b_{v}(s)$-metric spaces. Also, a modified version of a partial $b_{v}(s)$-metric space is defined and a fixed point theorem is proved in this space. Finally, some examples are given related to the results.

On Generalized Rational α − Geraghty Contraction Mappings in G − Metric Spaces

In this paper, we discuss about various generalizations of α − admissible mappings. Furthermore, we extend the concept of α − admissible to generalize rational α − Geraghty contraction in G − metric space. With this new contraction mapping, we establish some fixed-point theorems in G − metric space. The obtained result is verified with an example.

A NEW GENERALIZATION OF <inline-formula><tex-math id="M1">$ \mathcal{F} $</tex-math></inline-formula>-METRIC SPACES AND SOME FIXED POINT THEOREMS AND AN APPLICATION

<abstract> In this paper, we extend $ \mathcal{F} $-metric spaces to more general spaces, named generalized $ \mathcal{F} $-metric spaces and establish some fixed point theorems via comparison function, $ F $-contraction, Geraghty contraction and JS-contraction in the setting of generalized $ \mathcal{F} $-metric spaces. Our results generalize many present theorems. </abstract>

Fixed point results for Geraghty contraction type mappings in b-metric spaces

In this paper, we introduce some new results on the fixed point and common fixed points of Geraghty contraction mappings in b-metric b-complete spaces. Moreover, we give a representative example to illustrate the compatibility of our results.