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In this paper, we study the generalized F-iterated function system in G-metric space. Several results of common attractors of generalized iterated function systems obtained by using generalized F-Hutchinson operators are also established. We prove that the triplet of F-Hutchinson operators defined for a finite number of general contractive mappings on a complete G-metric space is itself a generalized F-contraction mapping on a space of compact sets. We also present several examples in 2-D and 3-D for our results.

The main goal of this work is to present GF -metric space, a new generalization of G-metric space. A comparison between the classes of G-metric spaces, GP-metric spaces, Gb-metric spaces, generalized Gb-metric spaces, and G∗ -metric spaces and the class of GF - metric spaces is also presented. We examine a few fundamental aspects of this newly defined abstract space. Proving the Banach contraction principle and the fixed point result for (ψ, ϕ)-contractive mapping in the context of GF -metric spaces is the paper’s secondary goal

We define expanded metric spaces, complete expanded metric space, and ɛ-continuous mapping in new ways and provide examples. Under the condition of ɛ-commuting mappings we study the existence and uniqueness of common fixed point theorems for a class of mappings in expexted metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we propose the notion of a distance between n points, called a g-metric, which is a further generalized G-metric. Indeed, it is shown that the g-metric with dimension 2 is the ordinary metric and the g-metric with dimension 3 is equivalent to the G-metric. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some common fixed point theorems using the concept of C class function in G-metric spaces. Moreover, some examples are presented to illustrate the validity of our results. [ABSTRACT FROM AUTHOR]

In this study, our aim is to demonstrate the formation of generalization of Gb-metric space, that is, extended Gb-metric space by means of the results of Kamran et al. [19]. We prove an analogue of Banach contraction principle and introduce outcomes in the framework of extended Gb-metric space. Various illustrations are given to describe our results. To show the usability, an application associated to our main result is also presented. [ABSTRACT FROM AUTHOR]

This paper aims to prove common fixed point theorems for a pair of hybrid and p-hybrid mappings via common limit range property in G-metric space setting. The theorems proved here will generalise the results due to Nashine et al. [35], Karapinar et al. [23, 24] from metric space notion to G-metric space and that of Mustafa et al.[30] using (CLRf ) property concept in G-metric space, and many others in this setting. We also provided an illustrative example to validate the results.

When working with a metric space, we are dealing with the additive group (R, +). Replacing (R, +) with an Abelian group (G, ∗), offers a new structure of a metric space. We call it a G-metric space and the induced topology is called the G-metric topology. In this paper, we are studying G-metric spaces based on L-groups (i.e., partially ordered groups which are lattices). Some results in G-metric spaces are obtained. The G-metric topology is defined which is further studied for its topological properties. We prove that if G is a densely ordered group or an infinite cyclic group, then every G-metric space is Hausdorff. It is shown that if G is a Dedekind-complete densely ordered group, (X, d) a G-metric space, A ⊆ X and d is bounded, then f : X → G with f(x) = d(x, A) := inf{d(x, a) : a ∈ A} is continuous and further x ∈ clXA if and only if f(x) = e (the identity element in G). Moreover, we show that if G is a densely ordered group and further a closed subset of R, K(X) is the family of nonempty compact subsets of X, e < g ∈ G and d is bounded, then d′ (A, B) < g if and only if A ⊆ Nd(B, g) and B ⊆ Nd(A, g), where Nd(A, g) = {x ∈ X : d(x, A) < g}, dB(A) = sup{d(a, B) : a ∈ A} and d′ (A, B) = sup{dA(B), dB(A)}.

In 2005, Lj. B. Ciric studied fixed points of asymptotically regular mappings [Math. Commun. 10(2005), 111-114]. The results of that study were extended by several authors. The aim of this article is to extend the main results to the context of g-metric spaces with order n, which was introduced by H. Choi, S. Kim, and S. Y. Yang in 2018 asymptotically regular mapping,

In this paper, we prove some common fixed point theorems for a pair of non-compatible faintly compatible self-mappings in G-metric spaces. Our results extend and unify some fixed points theorems in literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some coupled fixed point theorems for nonlinear contractive mappingsdo not having the mixed monotone property in partially ordered G-metric spaces.

In this paper, we reintroduce a class of compatible mappings namely ST-compatible mappings and prove some common fixed point theorems for two pairs of ST-compatible and weakly compatible mappings satisfying certain contractive conditions via C-class function in G-metric space. [ABSTRACT FROM AUTHOR]

In this paper, we consider the concept of non compatible mapping as property (E.A.) in G-metric space and prove some common fixed point theorems. [ABSTRACT FROM AUTHOR]

When working with a metric space, we are dealing with the additive group (R, +). Replacing (R, +) with an Abelian group (G, ∗), offers a new structure of a metric space. We call it a G-metric space and the induced topology is called the G-metric topology. In this paper, we are studying G-metric spaces based on L-groups (i.e., partially ordered groups which are lattices). Some results in G-metric spaces are obtained. The G-metric topology is defined which is further studied for its topological properties. We prove that if G is a densely ordered group or an infinite cyclic group, then every G-metric space is Hausdorff. It is shown that if G is a Dedekind-complete densely ordered group, (X, d) a G-metric space, A ⊆ X and d is bounded, then f: X → G with f(x) = d(x, A) := inf{d(x, a): a ∈ A} is continuous and further x ∈ clXA if and only if f(x) = e (the identity element in G). Moreover, we show that if G is a densely ordered group and further a closed subset of R, K(X) is the family of nonempty compact subsets of X, e < g ∈ G and d is bounded, then d′ (A, B) < g if and only if A ⊆ Nd(B, g) and B ⊆ Nd(A, g), where Nd(A, g) = {x ∈ X: d(x, A) < g}, dB(A) = sup{d(a, B): a ∈ A} and d′ (A, B) = sup{dA(B), dB(A)}. [ABSTRACT FROM AUTHOR]

In 2005, Lj. B. Ćirić studied fixed points of asymptotically regular mappings [Math. Commun. 10(2005), 111-114]. The results of that study were extended by several authors. The aim of this article is to extend the main results to the context of g-metric spaces with order n, which was introduced by H. Choi, S. Kim, and S. Y. Yang in 2018. [ABSTRACT FROM AUTHOR]

In this manuscript, we initiate the concept of rectangular α-G-admissible mappings with respect to β and we consider related type contractions in the setting of G-metric spaces. We provide some fixed point results. Also, some examples are given to support the obtained results. [ABSTRACT FROM AUTHOR]

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In this article some new fixed point and hybrid coincidence point theorems for multivalued mappings satisfying generalized contractive conditions have been proved in generalized metric spaces. Some nontrivial examples are given to support our main theorems. As application, a differential inclusion problem for heat conduction in metals has been given, using our main result, we prove the existence of solutions to the given differential inclusion problem. [ABSTRACT FROM AUTHOR]

We consider a triple (K; S; T) consisting of three nonlinear mappings defined on the union A ∪ B ∪ C of closed subsets of a generalized metric space. After introducing a notion of convex structure in the generalized metric space, we introduce the notion of tripartite contractions, tripartite semi-contractions, tripartite coincidence points, as well as tripartite best proximity points for the triple (K; S; T). We establish theorems on the existence and convergence of tripartite coincidence-best proximity points. Examples are given to support the new findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of common fixed point for three mappings in Gb-complete Gb-metric space. On the other hand, we prove that the theory is also established in G-metric space and several corollaries and examples are listed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some fixed point results using JS-G-contraction on G-metric spaces, also to prove some fixed point results on Gb-complete metric space for a new contraction. Our results extend and improve some results in the literature. Moreover, some examples are presented to illustrate the validity of our results.

Abstract In this paper, we use the concept of C-class functions to establish the best proximity point results for a certain class of proximal contractive mappings in S-metric spaces. Our results extend and improve some known results in the literature. We give examples to analyze and support our main results.

Abstract We present an analog of Banach’s fixed point theorem for C J M $CJM$ contractions in preordered metric spaces. These results substantially extend theorems of Ran and Reurings’ (Proc. Am. Math. Soc. 132(5): 1435-1443, 2003) and Nieto and Rodríguez-López (Order 22: 223-239, 2005).

Abstract Recently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012) introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction of research, in this paper, we present some new fixed point results for F-expanding mappings, especially on a complete G-metric space.

There are many fixed point results in the various kinds of metric spaces such as b - metric spaces, quaternion metric spaces, G-metric spaces, uniform spaces, non - commutative Banach spaces etc. In this work, we consider the one of modern methods as C*-algebra G-metric space with fixed point theory to solve problems above mentioned. We prove the fixed point theorems for a mapping under the contractive conditions in C*-algebra G-metric space. Besides, we establish the not only existence but also uniqueness theorem of fixed point in the such space. Also, we provide several examples to put support behind our main result.

In this work, we are interested to prove a general fixed point theorem for a mapping satisfying a new type of implicit relation in G-metric spaces. The results in this paper generalize the results obtained in [3], [7], [8], [10] and obtain other particular results. [ABSTRACT FROM AUTHOR]

In this paper, some coincidence and common fixed point theorems are established for two mappings satisfying a nonlinear contractive condition in G-metric spaces, generalizing and extending the work of Rashwan and Saleh [J. Nonlinear Convex Analysis, 7 (2006), 289-297]. We also give some examples to support the usability of our results. Moreover, it is proved that these mappings satisfy property Q. [ABSTRACT FROM AUTHOR]

In this paper, we utilize the family F and the notion of ω-distance in an ordered G-metric space and introduce (F, ω)-contractions in order to derive some fixed point results. We also discuss the problems of Ulam-Hyers stability, well-posedness and limit shadowing property. In order to illustrate the use of our results, we apply them to nonlinear integral equations, as well as to some three-point fractional integral boundary value problems, both with numerical examples. [ABSTRACT FROM AUTHOR]

Abstract In this paper, it is shown that the G -normed space introduced by K.A. Khan is not actually a generalization of normed linear space. In fact, every G -normed space is topologically the same as a normed linear space. To get over this situation a new notion of generalized norm in a linear space is introduced and its topological structure is studied. [ABSTRACT FROM AUTHOR]

The purpose of this article is to prove the convergence and stability of Mann and Ishikawa iterative procedures by applying λ-generalized, Geraghty and Ciric contractive conditions in a complete G-metric space. [ABSTRACT FROM AUTHOR]

In this paper, we prove the characterization of a Matkowski's theorem in the setting of quasi-metric spaces. As a result, we observe that some recent fixed point results in the context of G-metric spaces are

In this paper we use a specific function to investigate a new contraction in generalized probabilistic metric spaces. In this way, we establish certain fixed point theorems in recently introduced concept of generalized probabilistic metric spaces. Our result generalize/extend the existing results in literature. [ABSTRACT FROM AUTHOR]

We prove a common fixed point theorem for a pair of self mappings satisfying a generalized contractive type condition in a complete G-metric space. We also deal with other fixed point results for a self mapping in the setting of generalized metric space. Our results generalize some recent results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we derive and formulate many fixed point results of cyclic form under contractive conditions based on implicit relations in the setting of Ω-distance. Our results improve and generalize many existing results in the literature. Also, we introduce an example to show the validity of our main result.

We prove a common fixed point theorem for a pair of self mappings satisfying a generalized contractive type condition in a complete G-metric space. We also deal with other fixed point results for a self mapping in the setting of generalized metric space. Our results generalize some recent results in the literature

The aim of this paper is to prove coupled coincidence and coupled common fixed point theorems for a mixed ɡ-monotone mapping satisfying nonlinear contractive conditions in the setting of partially ordered G-metric spaces. Present theorems are true generalizations of the recent results of Choudhury and Maity [Math Comput. Modelling 54 (2011), 73-79], and Luong and Thuan [Math. Comput. Modelling 55 (2012), 1601-1609].

In this paper, we use the concept of C-class functions to establish the best proximity point results for a certain class of proximal contractive mappings in S-metric spaces. Our results extend and improve some known results in the literature. We give examples to analyze and support our main results. [ABSTRACT FROM AUTHOR]

Recently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012) introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction of research, in this paper, we present some new fixed point results for F-expanding mappings, especially on a complete G-metric space. [ABSTRACT FROM AUTHOR]

In this paper, we define new notions called (g-F) contractions and generalize Mizoguchi-Takahashi contractions for complete G-metric spaces and we establish some new coincidence points and common fixed point results. Our results unify and generalize various known comparable results from the current literature. An example and application are given to illustrate the usability of the main results. [ABSTRACT FROM AUTHOR]

Saadati et al [1] introduced the notion of Ω-distance mappings and studied some existing fixed point results. In this paper, we employ the notion of Ω-distance and some functions defined on [0,∞) to introduce some new nonlinear contractions of Suzuki types. We utilize our new notions toformulate and proved serval fixed and common fixed point results. Our results improve and extend many results in literature. [ABSTRACT FROM AUTHOR]

Best approximation results provide an approximate solution to the fixed point equation Tx = x, when the non-self mapping T has no fixed point. In particular a well- known best approximation theorem, due to Fan [6], asserts that if K is a nonempty compact convex subset of a Hausdor locally convex topological vector space E and T : K → E is a continuous mapping, then there exists an element x satisfying the condition d(x; Tx) = inf{d(y; Tx) : y ϵ K} where d is a metric on E. Recently, Hussain et al. (Abstract and Applied Analysis, Vol. 2014, Article ID 837943) introduced proximal contractive mappings and established certain best proximity point results for these mappings in G-metric spaces. The aim of this paper is to introduce certain new classes of auxiliary functions and proximal contraction mappings and establish best proximity point theorems for such kind of mappings in G-metric spaces. As consequences of these results, we deduce certain new best proximity and fixed point results in G-metric spaces. Moreover, we present certain examples to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper we present some coupled coincidence and coupled common fixed point theorems for mixed G-monotone mappings in partially ordered G-metric spaces.

In this paper, we prove some fixed point results involving α-implicit contractions in quasi-metric spaces. Moreover, we provide some known results on G-metric spaces. An example and an application on a solution of a nonlinear integral equation are also presented.

We prove a common fixed point theorem for a pair of self mappings in complete Gmetric spaces. Our result will improve and supplement some recent results in the setting of G-metric spaces.Probamos un teorema de punto fijo genérico para un par de auto-aplicaciones en espacios G-métricos completos. Nuestro resultado mejorará y complementará algunos de los resultados recientes en el marco de los espacios G-métricos.

We prove some fixed point theorems for self mappings satisfying some kind of contractive type conditions on complete G-metric spaces

In this paper, we introduce a new concept of (α, φ)g-contractive type mappings and establish coupled coincidence and coupled common fixed point theorems for such mappings in partially ordered G-metric spaces. The results on fixed point theorems are generalizations of some existing results.We also give some examples to illustrate the usability of the obtained results.

Using fixed point theory, we present a sufficient condition for the existence of a positive definite solution of the nonlinear matrix equation $${X = Q \pm \sum^{m}_{i=1}{A_{i}}^*F(X)A_{i}}$$ , where Q is a positive definite matrix, A 's are arbitrary n × n matrices and F is a monotone map from the set of positive definite matrices to itself. We show that the presented condition is weaker than that presented by Ran and Reurings [Proc. Amer. Math. Soc. 132 (2004), 1435-1443]. In order to do so, we establish some fixed point theorems for mappings satisfying ( $${\psi, \phi}$$ )-weak contractivity conditions in partially ordered G-metric spaces, which generalize some existing results related to ( $${\psi, \phi}$$ )-weak contractions in partially ordered metric spaces as well as in G-metric spaces for a given function f. We conclude, by presenting an example, that our fixed point theorem cannot be obtained from any existing fixed point theorem using the process of Jleli and Samet [Fixed Point Theory Appl. 2012 (2012), Article ID 210]. [ABSTRACT FROM AUTHOR]

In this manuscript, common fixed point results for self-mappings satisfying generalized weak integral type contraction in the setting of G-metric space are established. Using the derived results, some applications to the systems of non-linear integral and fractional differential equations are also discussed. [ABSTRACT FROM AUTHOR]