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The notion of triangular inequality plays an important role in determining the structure of distance spaces. In particular, the structure of fuzzy metric spaces depends on the triangular inequality and the concerned t-norm. In most of the fixed point theorems in fuzzy metric spaces both the triangular inequality and the concerned t-norm have a major impact on the proof of fixed point theorems. Inspired by the concept of graphical metric space, it was recently introduced in N. Saleem et al., On Graphical Fuzzy Metric Spaces with Application to Fractional Differential Equations, Fractal and Fract., 6:5 (2022), 238:1-12, the notion of graphical fuzzy metric space and proved some fixed point results. The triangular inequality in such spaces is replaced by a weaker one which is directly associated with the graphical structure affine with the space. In this paper some observations on the recent results of Saleem et al. are made and so the results are revisited. Some related topological properties with some new fixed point results in graphical fuzzy metric spaces are also proved. The results of this paper generalize and extend Banach contraction principle and some other known results in this new setting. Several examples are given which support the claims and illustrate the significance of the new concepts and results. [ABSTRACT FROM AUTHOR]

In the present paper, under certain assumptions, we establish the convergence of iterates for self-mappings of complete metric spaces with graphs which are of a contractive type. The class of mappings considered in the paper contains the so-called cyclical mappings introduced by W. A. Kirk, P. S. Srinivasan and P. Veeramani in 2003 and the class of monotone nonexpansive operators. Our results hold in the case of a symmetric graph. [ABSTRACT FROM AUTHOR]

It is known that a strict contraction on complete metric spaces with graphs possesses a fixed point. In the present paper we show that this property holds for mappings on complete metric spaces with graphs which are merely contractive. We also obtain some stability results. [ABSTRACT FROM AUTHOR]

In 1988 N.A. Assad showed that a nonself nonlinear contraction taking a closed subset of a complete metrically convex space into the space so that the boundary of this subset is mapped back into the subset itself has a unique fixed point. In the present paper we extend this result by replacing the complete metrically convex space with a complete metric space which is a length space. [ABSTRACT FROM AUTHOR]

In this work, we study an iterative process induced by a contractive type set-valued mapping in a complete metric space and show its convergence, taking into account computational errors. [ABSTRACT FROM AUTHOR]

It is known that a strict contraction on a complete metric space with a graph possesses a fixed point. In the present paper, we show that this property holds for single valued and set-valued self-mappings of metric spaces with graphs that are of the contractive type. We also show the convergence of iterates of these mappings to fixed points. In particular, our results are true for metric spaces with symmetric graphs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of α -- ψ -- f-contractive mappings and get some new common fixed point results, in particular, generalized Lipschitz condition for such mappings in cone metric spaces over Banach algebras. Also, we support our results by some examples. [ABSTRACT FROM AUTHOR]

In this article, we extend some recently fixed point theorems in the setting of G-fuzzy metric spaces. We introduce some new concepts of contractions called γ-contractions and γ-weak contractions. We prove some fixed point theorems for mappings providing γ-contractions and γ-weak contractions. On the other hand, we consider a more general class of auxiliary functions in the contractivity condition. [ABSTRACT FROM AUTHOR]

This paper aims to establish some fixed point results for a new class of contractive type mappings in fuzzy metric-like spaces. The results of this paper generalize and extend the Banach contraction principle and some other known results in the setting of fuzzy metric-like spaces. [ABSTRACT FROM AUTHOR]

In this manuscript, We introduce some fixed point results for some contractive type mappings on complete ordered triangular neutrosophic metric spaces, and review many existing results in the literature. Furthermore, we use our results to obtain the property (P).

In the present paper, under certain assumptions, we establish the convergence of iterates for self-mappings of complete metric spaces with graphs which are of a contractive type. The class of mappings considered in the paper contains the so-called cyclical mappings introduced by W. A. Kirk, P. S. Srinivasan and P. Veeramani in 2003 and the class of monotone nonexpansive operators. Our results hold in the case of a symmetric graph.

In the present paper, we introduce a new three-step fixed point iteration called SNIA-iteration (Naveen et al. iteration) which converges faster than the original iteration. It is possible by introducing a contraction operator on the existing iteration algorithm where the coefficients of the new iterative process are chosen in (1 2 , 1) instead of [0, 1]. The strong convergence result for the SNIA-iteration method is also proved by showing the convergence of this iteration method towards its fixed point. Further, the coefficients involved in SNIA-iteration have been interchanged, and then the result is compared with the original iteration. It is found that the new result is better than the previous one in the sense of its rate of convergence for contraction mappings. [ABSTRACT FROM AUTHOR]

In this paper, a new type of contraction mapping is introduced, called generalized quasi like contractive mapping, and three types of new iterative schemes are presented as multi_L_explicit four step iteration, multi_ L_ explicit Noor iteration and multi_ L_Picard s-iteration. We study the rate of convergence and stability with generalized quasi like contractive mapping [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of weak Wardowski contractive multivalued mappings and investigate the solvability of generalized '-Caputo snap boundary fractional differential inclusions. Our results utilize some existing results regarding snap boundary fractional differential inclusions. An example is given to illustrate the applicability of our main results. [ABSTRACT FROM AUTHOR]

In this manuscript, We introduce some fixed point results for some contractive type mappings on complete ordered triangular neutrosophic metric spaces, and review many existing results in the literature. Furthermore, we use our results to obtain the property (P). [ABSTRACT FROM AUTHOR]

In this paper we present some suggestions for unifying the terminology of the mappings appearing in fixed point iterative methods for the case when the setting is a metric space. We consider the following concepts: contraction type mapping, contractive type mapping and nonexpansive type mapping, for which some problems are formulated. [ABSTRACT FROM AUTHOR]

In this work, we study an iterative process induced by a contractive type set-valued mapping in a complete metric space and show its convergence, taking into account computational errors.

It is known that a strict contraction on a complete metric space with a graph possesses a fixed point. In the present paper, we show that this property holds for single valued and set-valued self-mappings of metric spaces with graphs that are of the contractive type. We also show the convergence of iterates of these mappings to fixed points. In particular, our results are true for metric spaces with symmetric graphs.

This paper is concerned with the asymptotic behavior of solutions of linear differential-algebraic equations (DAEs) under small nonlinear perturbations. Some results on the asymptotic behavior of solutions which are well known for ordinary differential equations are extended to DAEs. The main tools are the projector-based decoupling and the contractive mapping principle. Under certain assumptions on the linear part and the nonlinear term, asymptotic behavior of solutions are characterized. As the main result, a Perron type theorem that establishes the exponential growth rate of solutions is formulated.

In this work, a new common fixed point result by generalized contractive functions fulfilling the type of admissibility condition in a Hausdorff Branciari metric space with the support of C-functions, was obtained.

In this paper, we introduce the notion of weak Wardowski contractive multivalued mappings and investigate the solvability of generalized '-Caputo snap boundary fractional differential inclusions. Our results utilize some existing results regarding snap boundary fractional differential inclusions. An example is given to illustrate the applicability of our main results.

In this paper, we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in τ-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove some existence and uniqueness theorems of the fixed points for Hardy-Rogers type contraction with respect to a wt-distance in b-metric spaces endowed with a graph. These results prepare a more general statement, since we apply the condition of orbitally G-continuity of mappings instead of the condition of continuity, consider b-metric spaces endowed with a graph instead general b-metric spaces and use of control functions instead of constant numbers. [ABSTRACT FROM AUTHOR]

The principal object of this paper is to present new contractive type condition for mappings defined on G-metric spaces. Further, we prove some new fixed point theorems concerning these mappings in G-metric space. Particular cases and examples to illustrate and support our results are also considered. Our findings extend and unify a known results. [ABSTRACT FROM AUTHOR]

Abstract We prove the existence and uniqueness of fixed points of some generalized contractible operators defined on modular G-metric spaces and also prove the modular G-continuity of such operators. Furthermore, we prove that some generalized weakly compatible contractive operators in modular G-metric spaces have a unique fixed point. Our results extend, generalize, complement and include several known results as special cases.

In the current work, we broaden the class of C* -algebra-valued hexagonal b-metric spaces and C* -algebra-valued extended b-metric spaces by defining the class of C*-algebra-valued extended hexagonal b-metric spaces and demonstrate a fixed point theorem with distinct contractive condition. In addition, an application is presented in the later part to demonstrate the existence and uniqueness of a particular type of operator equation in order to elucidate our results. [ABSTRACT FROM AUTHOR]

Recently, fixed point results via E -contractions (also called P- contractions in some papers) for self-mappings in metric spaces have been investigated. Some results generalize the well - known Edelstein's theorem. In this paper, we provide some new fixed point theorems for mappings satisfying conditions of Edelstein - Suzuki type involving E -contractions. We also present several illustrative examples to compare our finding with some know results in the literature. [ABSTRACT FROM AUTHOR]

Here, some fixed point theorems in partially ordered spaces are proved. As an application, the existence of a solution of an integral equation is obtained. [ABSTRACT FROM AUTHOR]

The major motives of this paper are to study different types of contractive mappings and also to answer an open question of Garai et al. [Some remarks on bv(s)-metric spaces and fixed point results with an application]. We first set up some fixed point results associated with two types of contractive mappings in bv(s)-metric spaces and then we give an answer, in positive, to the open question. Most importantly, we characterize the completeness of a bv(s)-metric space via fixed point property of a certain type of contractive mappings. Our results extend and generalize several important results in the literature. [ABSTRACT FROM AUTHOR]

Purpose – The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases. Design/methodology/approach – The results of this paper are theoretical and analytical in nature. Findings – The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases. Research limitations/implications – The results are theoretical and analytical. Practical implications – The results were applied to solving nonlinear integral equations. Social implications – The results has several social applications. Originality/value – The results of this paper are new.

In 1970, Cesàro sequence spaces was introduced by Shiue. In 1981, Kızmaz defined difference sequence spaces for ℓ∞, c0 and c. Then, in 1983, Orhan introduced Cesàro difference sequence spaces. Both works used difference operator and investigated the Köthe--Toeplitz dual for the new Banach spaces they introduced. Later, various authors generalized these new spaces, especially the one introduced by Orhan. In this study, first we discuss the fixed point property for these spaces and for the corresponding function space of the Köthe--Toeplitz dual. Moreover, we consider another generalized space which is a degenerate Lorentz space because the spaces we consider are somehow related in terms of their construction. In fact, the Köthe--Toeplitz dual is contained in ℓ¹, the corresponding function space contains Lebesgue space, the Banach space of Lebesgue integrable functions on [0, 1], L1[0, 1] but for the degenerate Lorentz space and its corresponding function space, this is reversed completely. Then, as an important result, for both function spaces we show that they fail the weak fixed point property for isometries and even for contractions. As the second main result, by passing to counting measure, we take the corresponding sequence spaces, and for both spaces we get large classes of closed, bounded and convex subsets satisfying the fixed point property for nonexpansive mappings as a Goebel and Kuczumow analogy after noting that in ℓ¹ Goebel and Kuczumow found a large class with the fixed point property for nonexpansive mappings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new notions in a soft metric space. We study a fixed soft point under generalized contractive conditions without mappings continuity. Further, we prove some results related to our generalization. Moreover, we provide one example to present the application [ABSTRACT FROM AUTHOR]

In [6], Moudafi introduced the so-called viscosity iterative method to approximate a fixed point of a nonexpansive mapping and proved the strong convergence of the generated sequence. Since then, several authors extended the convergence result in different settings and for mappings satisfying general metric conditions. Anyway, to the best of our knowledge and beside numerical simulations, little is known about the speed of convergence of the method itself. In this paper, we propose a step in this direction by giving an estimate for the rate of convergence of viscosity sequences generated by quasi-nonexpansive mappings in the setting of q-uniformly smooth Banach spaces. [ABSTRACT FROM AUTHOR]

Ran and Reurings (Proc Am Math Soc 132(5):1435–1443, 2003) extended the Banach contraction principle to the setting of partially ordered metric spaces and recently Proinov (J Fixed Point Theory Appl 22:21, 2020) extended and unified many earlier fixed point theorems. In this paper we will present analogous results for the significantly wider class of mappings on preordered metric spaces. We give non-trivial examples of Kannan-type mappings. [ABSTRACT FROM AUTHOR]

We prove the existence and uniqueness of fixed points of some generalized contractible operators defined on modular G-metric spaces and also prove the modular G-continuity of such operators. Furthermore, we prove that some generalized weakly compatible contractive operators in modular G-metric spaces have a unique fixed point. Our results extend, generalize, complement and include several known results as special cases. [ABSTRACT FROM AUTHOR]

We have recently established the existence of a unique fixed point for nonlinear contractive self-mappings of a closed subset of a Banach space, which is not necessarily bounded. In this paper, we extend this result to contractive mappings, which map a closed subset of a Banach space into the space. [ABSTRACT FROM AUTHOR]

We first introduce a novel notion named C*-algebra-valued bv(s)-metric spaces. Then, we give proofs of the Banach contraction principle, the expansion mapping theorem, and Jungck's theorem in C*-algebra-valued bv(s)-metric spaces. As an application of our results, we establish a result for an integral equation in a C*-algebra-valued bv(s)-metric space. Finally, a numerical method is presented to solve the proposed integral equation, and the convergence of this method is also studied. Moreover, a numerical example is given to show applicability and accuracy of the numerical method and guarantee the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the topological dimension of the set of solutions of the operator inclusion of the form , where A is a bounded linear surjective operator, and F is a multi-valued Lipschitz map with closed convex images. The resulting theorem establishes a connection between the dimension of the kernel of the operator A and the dimension of the set of solutions of this inclusion. [ABSTRACT FROM AUTHOR]

In this paper, we present some fixed point theorems for a class of contractive mappings in complete b-metric spaces of zero at infinity varieties. We verify the T-stability of Picard's iteration and the P property for such mapping. [ABSTRACT FROM AUTHOR]