G-metric Spaces Research Articles

Control Functions in G-Metric Spaces: Novel Methods for θ-Fixed Points and θ-Fixed Circles with an Application

The purpose of this paper is to present some new contraction mappings via control functions. In addition, some fixed point results for Θ,α,θ,Ψ contraction, rational Θ,α,θ,Ψ contraction and almost Θ,α,θ,Ψ contraction mappings are obtained. Moreover, under contraction mappings of types (I), (II), and (III) of Θ,θ,Ψυ0, several fixed circle solutions are provided in the setting of a G-Metric space. Our results extend, unify, and generalize many previously published papers in this direction. In addition, some examples to show the reliability of our results are presented. Finally, a supporting application that discusses the possibility of a solution to a nonlinear integral equation is incorporated.

Solution of an integral equation in G-metric spaces

In this paper, we prove a fixed point result in G-metric spaces satisfying generalized contractive condition with new auxiliary functions, which generalize the result of Bhardwaj and Kumar. The motivation of this paper is to observe the solution of an integral equation using the fixed point technique in G -metric space.

New convergence definitions for double sequences in g-metric spaces

New convergence definitions for double sequences in g-metric spaces

G-metric spaces and the related approximate fixed point results

G-metric spaces and the related approximate fixed point results

Fixed Point Theorems for Sub–Compatible and Sub–Sequential Continuous Maps in G-Metric Space

Fixed Point Theorems for Sub–Compatible and Sub–Sequential Continuous Maps in G-Metric Space

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.

Coupled fixed point theorems of JS-G-contraction on G-metric spaces

Jaradat has proven some fixed point results using JS-G-contraction on $G-$metric spaces. Choudhury et al. were derived coupled fixed point theorems for the $G-$metric spaces. The purpose of this paper is to prove some coupled fixed point theorems of JS-G-contraction on G-metric spaces. Moreover, some example is presented to illustrate the validity of our results.

RATIONAL TYPE CONTRACTION MAPPING THEOREMS ON MULTIPLICATIVE G-METRIC SPACES

In this article, we have extended the results of Y. U. Gaba by taking multiplicative G-metric space instead of G-metric space. In this way, we proved contraction mapping theorems on multiplicative, G-metric spaces using rational type contraction conditions for a single map. Later on, we extended our results in the settings of triplet maps. We have also given examples to support our results.

Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-Metric Spaces with Applications

In this paper, we introduce a generalized Δ-implicit locally contractive condition and give some examples to support it and show its significance in fixed point theory. We prove that the mappings satisfying the generalized Δ-implicit locally contractive condition admit a common fixed point, where the ordered multiplicative GM-metric space is chosen as the underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show the existence of solutions to a system of nonlinear—Volterra type—integral equations.

Various fixed-points results of picard sequence in complete G - metric space

We are demonstrating some new fixed-point theorems associated with Picard sequence in G-metric spaces. We establish consequences of Khojasteh et al. [6] for single-valued mappings in G-metric spaces. We clarify our result by giving an example.

On Certain Quadruple Fixed Points of Integral Type Contraction Mappings in G-Metric Spaces and its Applications

In this paper, the existence of common quadruple fixed point results for integral type contraction of two mappings in G-metric spaces is established. Some interesting consequences of our results are achieved. Moreover, we give an illustration that presents the applicability of the achieved results.

Fixed point results for generalized rational contractions in complex valued G-metric spaces

In present article, we demonstrate some fixed point results for generalized rational contractions in complex valued g-metric space. Our outcomes extend and generalize various famous results in the literature.

Fixed point theorems for modified generalized F-contraction in G-metric spaces

In this paper, we introduce new notions of generalized F-contractions of type(S) and type(M) in G-metric spaces. Some common fixed point theorems are proved using these notions. A suitable example is also provided to support our results.

Statistical convergence in g-metric spaces

The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.

Fixed point theory for simulation functions in G-metric spaces: A novel approach

In this paper, with the aid of simulation mapping 𝜂: [0,∞) × [0,∞)->ℝ, we prove some Lemmas and fixed point result for generalized 𝒵 − contraction of the mapping 𝑔: 𝑋->𝑋 satisfying the following conditions: 𝜂(𝒢(𝑔𝑥, 𝑔𝑦, 𝑔𝑧),ℳ(𝑥, 𝑦, 𝑧)) ≥ 0, for all 𝑥, 𝑦, 𝑧 ∈ 𝑋, where ℳ(𝑥, 𝑦, 𝑧) = max {𝒢(𝑥, 𝑔𝑦, 𝑔𝑦), 𝒢(𝑦, 𝑔𝑥, 𝑔𝑥), 𝒢(𝑦, 𝑔𝑧, 𝑔𝑧), 𝒢(𝑧, 𝑔𝑦, 𝑔𝑦), 𝒢(𝑧, 𝑔𝑥, 𝑔𝑥), 𝒢(𝑥, 𝑔𝑧, 𝑔𝑧)}. and (𝑋, 𝒢) is a 𝒢 − metric space. An example is also given to support our results.

Approximate fixed points of operators on modular G-metric spaces

In this paper, we will first introduce the approximate fixed point property and a new class of operators and contraction mapping for a cyclic map T on modular G-metric spaces. Also, we prove two general lemmas regarding approximate fixed Point of cyclic maps on modular G-metric spaces. Using these results we prove several approximate fixed point theorems for a new class of operators and contraction mapping on modular G-metric spaces.

Fixed Point Theorem in G-Metric Space for Auxiliary Functions

In this paper, fixed point results satisfying generalized contractive condition with new auxiliary functions are proved in \(G\)-metric spaces.

Multivalued (g − F − φ) contractions obtaining common fixed points inG-metric spaces

The aim of this paper is to introduce new notions called generalized [Formula: see text] contraction and rational type [Formula: see text] contraction for hybrid maps in complete G-metric spaces. First, using new concept of generalized [Formula: see text] contraction we establish a common fixed point theorem for a hybrid pair of weakly compatible maps. Second, we prove a common fixed point theorem for occasionally coincidentally idempotent mappings satisfying another new concept of rational type [Formula: see text] contraction under common limit range property. Our results generalize and improve several known results of the existing literature. Also, we give an example to indicate the usefulness of our main results.

Fixed point theorem with contractive mapping on C*-Algebra valued G-Metric Space

Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T : X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C *-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C *-algebra valued G-metric space is a generalization of the G-metric space and the C*-algebra valued metric space, meanwhile the G-metric space and the C *-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X × X into X × X × X, the C *-algebra valued metric generalized the codomain from real number into C *-algebra, and the C *-algebra valued G-metric space generalized both the domain and the codomain. In C *-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C *-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)}.

C*-Algebra Valued Modular G-Metric Spaces with Applications in Fixed Point Theory

This article introduces a new type of C*-algebra valued modular G-metric spaces that is more general than both C*-algebra valued modular metric spaces and modular G-metric spaces. Some properties are also discussed with examples. A few common fixed point results in C*-algebra valued modular G-metric spaces are discussed using the “C*-class function”, along with some suitable examples to validate the results. Ulam–Hyers stability is used to check the stability of some fixed point results. As applications, the existence and uniqueness of solutions for a particular problem in dynamical programming and a system of nonlinear integral equations are provided.