Geraghty Type Research Articles

Fixed point results of Geraghty type contractions with equivalent distance

In this manuscript, we present the concept of E -Geraghty contractions, demonstrating several fixed point results.Additionally, we provide an illustrative example to highlight our principal findings.

Some Geraghty Type Inequalities in b-fuzzy Metric Spaces with an Application

In this note, we introduce novel Geraghty-type inequalities within the framework of a b-fuzzy metric space and develop new fixed point theorems for such mappings in a G-complete b-fuzzy metric space. To substantiate our findings, we present several illustrative examples using graphical methods. Additionally, we demonstrate the application of our introduced theorems by solving a non-linear integral equation, showing the practical utility of our results.

Fixed Point Results for Geraghty Type Contractions in Extended Rec-tangular Fuzzy <i>b</i>-metric Space with an Application

The aim of this paper is to define the notions of extended fuzzy b-metric spaces, fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces and to establish certain fixed point results in these settings utilizing Geraghty type contractions. We also furnished an example which illustrates our main result. To show the authenticity of our results we provide an application involving fuzzy integral equation. The obtained results generalize many existing results in the literature.

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.

Geraghty Type Contractions in Relational Metric Space with Applications to Fractional Differential Equations

The present manuscript is devoted to investigating some existence and uniqueness results on fixed points by employing generalized contractions in the context of metric space endued with a weak class of transitive relation. Our results improve, modify, enrich and unify several existing fixed point theorems, The results proved in this study are utilized to find a unique solution of certain fractional boundary value problems.

Solution of integral equations for multivalued maps in fuzzy $ b $-metric spaces using Geraghty type contractions

<abstract><p>In this article, the notion of Hausdorff fuzzy $ b $-metric space is studied. Some fixed point results for multivalued mappings using Geraghty type contractions in $ G $-complete fuzzy $ b $-metric spaces are established. To strengthen the results, an illustrative example is furnished. A fuzzy integral inclusion is constructed as an application of fixed point result which shows the validity of the proved results. The presented outcomes are the generalization of the existing results in literature.</p></abstract>

Fixed point results for a new multivalued Geraghty type contraction via CG-simulation functions

The aim of this paper is to introduce the new concept of a multivalued Geraghty type contraction mapping using CG-simulation functions and C-class functions. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. As consequences, we arrive at fixed point results endowed with graph. To demonstrate the credibility of our results, we give an example that proves it.

Fixed point results for a new $ \alpha $-$ \theta $-Geraghty type contraction mapping in metric-like space via $ \mathcal{C}_\mathcal{G} $-simulation functions

<abstract><p>This paper aims to introduce the new concept of an $ \alpha $-$ \theta $-Geraghty type contraction mapping using $ \mathcal{C}_{\mathcal{G}} $-simulation in a metric-like space. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. We provide some examples as an application that proves the credibility of our results.</p></abstract>

Nonlinear contractions and Caputo tempered implicit fractional differential equations in b-Metric spaces with infinite delay

This paper deals with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-Metric spaces with initial condition and infinite delay. The results are based on the ???-Geraghty type contraction, the F-contraction and the fixed point theory. Furthermore, an two illustrations are presented to demonstrate the plausibility of our results.

Existence of fixed points in G-metric spaces

In this manuscript, we provide some new results for the existence of fixed points for a certain contractive condition of Geraghty type in the setting of partially ordered $G$-metric space. Also, we provide an example to illustrate the usability of results. Our results generalize or extend many well known results in the literature.

Solution to Integral Equation in an O-Complete Branciari b-Metric Spaces

In this paper, we prove fixed point theorem via orthogonal Geraghty type α-admissible contraction map in an orthogonal complete Branciari b-metric spaces context. An example is presented to strengthen our main result. We provided an application to find the existence and uniqueness of a solution to the Volterra integral equation. We have compared the approximate solution and exact solution numerically.

Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions

In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions of Geraghty type. Additionally, in the year 2021, Beg et al. introduced the concept of generalized F-proximal contraction of the first kind and generalized F-proximal contraction of the second kind, respectively. After developing these concepts, authors mainly studied the best proximity points for these classes of mappings. In this short note, we prove that the problem of the existence of the best proximity points for the said classes of proximal contractions is equivalent to the corresponding fixed points problems.

Fixed point problem of a multi-valued Kannan–Geraghty type contraction via w-distance

Fixed point problem of a multi-valued Kannan–Geraghty type contraction via w-distance

Fixed point results of $$\beta _Y$$-Geraghty type contractive mapping in modular metric-like spaces

Fixed point results of $$\beta _Y$$-Geraghty type contractive mapping in modular metric-like spaces

A unification of Geraghty type and Ciric type fixed point theorems

In the framework of metric spaces, we introduce the concept of Geraghty-Ciric type contractions and show the existence and uniqueness of the fixed point of such mappings. This result improves and unifies those obtained by Geraghty (Proc. Amer. Math. Soc. 40, 604-608 (1973)) and Ciric (Proc. Amer. Math. Soc. 45, 267-273, (1974)). Several technical lemmas are employed to ensure that a Picard sequence is a Cauchy sequence. In addition, two illustrative examples are provided to indicate the validity of the obtained results.

On Geraghty $ \perp $-contractions in $ O $-metric spaces and an application to an ordinary type differential equation

<abstract><p>By combining the concept of orthogonality and the Geraghty type contraction, we give some fixed point results in the class of $ O $-metric spaces. Our obtained results extend the existing results in the literature. We also resolve an ordinary type differential equation.</p></abstract>

Infinite Geraghty type extensions and their applications on integral equations

In this article, we discuss about a series of infinite dimensional extensions of some theorems given in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018), (Fisher in Math. Mag. 48(4):223–225, 1975), and (Fogh, Behnamian and Pashaie in Int. J. Maps in Mathematics 2(41):1–13, 2019). We also prove a similar Geraghty type construction for Fisher (Math. Mag. 48(4):223–225, 1975) in an infinite dimension using similar techniques as in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018) and (Fogh, Behnamian and Pashaie in Int. J. Maps in Mathematics 2(41):1–13, 2019). As an application, we ensure the existence of solutions for infinite dimensional Fredholm integral equation and Uryshon type integral equation.

New Fixed Point Results for Generalized Θ-Contraction in Extended 𝐆𝐛-Metric Spaces with an Application

Through this work, we analyze the structure of extended Gb-metric spaces and show a fundamental lemma for sequence convergence within the same metric. We also propose the new notion of generalized geraghty type Θ-berinde contraction mappings and demonstrate several fixed point theorems for these mappingsin the sense of extended Gb-metric spaces. Eventually, the existence result for solutions of a Fredholm integral equation is furnished to show the efficacy of the technique developed.

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.

Common Fixed Point Results for Almost ℛg-Geraghty Type Contraction Mappings in b2-Metric Spaces with an Application to Integral Equations

In this paper, we define almost Rg-Geraghty type contractions and utilize the same to establish some coincidence and common fixed point results in the setting of b2-metric spaces endowed with binary relations. As consequences of our newly proved results, we deduce some coincidence and common fixed point results for almost g-α-η Geraghty type contraction mappings in b2-metric spaces. In addition, we derive some coincidence and common fixed point results in partially ordered b2-metric spaces. Moreover, to show the utility of our main results, we provide an example and an application to non-linear integral equations.