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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 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]

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 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.

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.

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 [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]

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]

We compare the newly defined bv(s)-metric spaces with several other abstract spaces like metric spaces, b-metric spaces and show that some well-known results, which hold in the latter class of spaces, may not hold in bv(s)-metric spaces. Besides, we introduce the notions of sequential compactness and bounded compactness in the framework of bv(s)-metric spaces. Using these notions, we prove some fixed point results involving Nemytzki–Edelstein type mappings in this setting, from which several comparable fixed point results can be deduced. In addition to these, we find some existence and uniqueness criteria for the solution to a certain type of mixed Fredholm–Volterra integral equations.

Change detection in heterogeneous bitemporal satellite images has become an emerging, important, and challenging research topic in remote sensing for rapid damage assessment. In this article, we explore a new parametric mapping strategy based on a modified geometric fractal decomposition and a contractive mapping approach allowing us to project the before image on any after imaging modality type. This projection exploits the fact that any satellite image data can be approximatively encoded in terms of spatial self-similarities at different scales and this property remains quite invariant to a given imaging modality type. Once the projection is performed and that a pixelwise difference map between the two images (presented in the same imaging modality) is then binarized in the unsupervised Bayesian framework. At this stage, we will test several parameter estimation procedures combined with several segmentation strategies based on different Bayesian cost functions. The experiments for change detection, with real images showing different multimodalities and changed events, indicate that this new fractal-based projection method, which is entirely based on a series of structural and spatial information, is an interesting alternative to classical regression-based projection methods (based only on luminance transformation). Besides, the experiments also show that the difference map, resulting in this novel projection strategy, is also particularly amenable for an unsupervised Markovian binarization approach. [ABSTRACT FROM AUTHOR]

We compare the newly defined bv(s)-metric spaces with several other abstract spaces like metric spaces, b-metric spaces and show that some well-known results, which hold in the latter class of spaces, may not hold in bv(s)-metric spaces. Besides, we introduce the notions of sequential compactness and bounded compactness in the framework of bv(s)-metric spaces. Using these notions, we prove some fixed point results involving Nemytzki-Edelstein type mappings in this setting, from which several comparable fixed point results can be deduced. In addition to these, we find some existence and uniqueness criteria for the solution to a certain type of mixed Fredholm-Volterra integral equations. [ABSTRACT FROM AUTHOR]

In this short note, we state some crucial facts which have to be accompanied in a series of results in the literature. Furthermore, the aim of this paper is to warn researchers to be cautious in modeling different problems governed by expansive or contractive type mappings, in the setting of a bounded metric space. [ABSTRACT FROM AUTHOR]

We establish fixed point, stability and genericity theorems for strict contractions on complete metric spaces with graphs.

In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ, θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented. First Published Online: 21 Nov 2018

In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (2012), Piri and Kumam (2016), Secelean (2016), Proinov (2020), and others are consequences of our main result. An application in integral equations and some illustrative examples are indicated.

In this paper, fixed point theorems using ψ contractive mapping in C∗-algebra valued b-metric space are introduced. By stating multiple scenarios that illustrate the application domains, we demonstrate several applications from the obtained results. In particular, we begin with the definition of the positive function and then recall some properties of the function that lay the fundamental basis for the research. We then study some fixed point theorems in the C∗-algebra valued b-metric space using a positive function.

In a recent work, we established the existence of a unique fixed point for nonlinear contractive self-mappings of a bounded and closed set in a Banach space. In the present paper we extend this result to the case of unbounded sets.

In this paper, we obtain some fixed point theorems for dominated mappings satisfying locally contractive conditions on a closed ball in a left K-sequentially O-complete ordered quasi-partial metric space and in a right K-sequentially O-complete ordered quasi-partial metric space, respectively. Our results improve several well known results.

In this paper, we present some fixed point results in the setting of a complete metric spaces by defining a new contractive condition via admissible mapping embedded in simulation function. [ABSTRACT FROM AUTHOR]

We introduce a new concept of α-fuzzy H-contractive mapping which is essentially weaker than the class of fuzzy contractive mapping and stronger than the concept of α-ϕ-fuzzy contractive mapping. For this type of contractions, the existence and uniqueness of fixed point in fuzzy M-complete metric spaces is also established. [ABSTRACT FROM AUTHOR]

By using the idea of Pata [V. Pata, A fixed point theorem in metric spaces. J. Fixed Point Theory Appl. 10 (2011) 299-305.] we establish a new common fixed point theorem and as an application, we prove the existence and uniqueness of common solutions for a class of system of functional equations arising in dynamic programming. [ABSTRACT FROM AUTHOR]

In this paper, by using generalized viscosity mappings, we prove two strong convergence theorems for finding fixed points of a nonexpansive mapping which is also a unique solution of the variational inequality. Our results extend and improve the recent ones announced by some authors. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish the structure of C*- algebra-valued b2-metric space and give some fixed point theorems for self-maps with contractive or expansive conditions on such spaces. As an application we investigate existence and uniqueness solution for a type of integral equation. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new contractive condition. We prove the existence and uniqueness of a fixed point of self-mapping under this new contractive condition. Moreover, we observe analog of these results for the mappings that satisfy the property P. An application on integral equations is presented to illustrate the main result. Our results extend and generalize well-known results in the literature. [ABSTRACT FROM AUTHOR]

In a real uniformly convex and uniformly smooth Banach space, we first prove a new path convergence theorem and then present some new semi-implicit iterative schemes with errors which are proved to be convergent strongly to the common element of the set of zero points of infinite m-accretive mappings and the set of fixed points of infinite nonexpansive mappings. The superposition of perturbed operators are considered in the construction of the iterative schemes and new proof techniques are employed compared to some of the recent work. Some examples are listed and computational experiments are conducted, which guarantee the effectiveness of the proposed iterative schemes. Moreover, a kind of parabolic systems is exemplified, which sets up the relationship among iterative schemes, nonlinear systems and variational inequalities. [ABSTRACT FROM AUTHOR]

Meir and Keeler formulated their fixed point theorem for contractive mappings with purely metric condition. This idea was extended by numerous mathematicians. In this paper, we present a simple method of proving such theorems and give new results. [ABSTRACT FROM AUTHOR]