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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 paper, we introduce the notion of generalized weakly contractive mapping of quadratic type and we prove fixed point results for this type of mapping. We justify our result by suitable examples and show that this mapping satisfies properties P and Q. Among other things, as corollaries we recover Banach and Kannan fixed point theorems. [ABSTRACT FROM AUTHOR]

Z. D. Mitrović and S. Radenović introduced in [The Banach and Reich contractions inbv(s)-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 3087–3095] a new class of generalized metric spaces and proved some fixed point theorems in this framework. The purpose of this paper is to consider other kinds of contractive mappings in bv(s)-metric spaces, and show how the work in the new settings differs from the one in standard metric and b-metric spaces. Examples show the usefulness of the obtained results. [ABSTRACT FROM AUTHOR]

In the present work, we first establish the notion of extended hexagonal b-metric space and demonstrate some fixed point theorems with various contractive conditions using a new class of comparison functions. In order to justify the newly invented results, we have provided some interesting examples to enhance the understanding of the proven theory. Secondly, to illustrate our results an application is offered to the existence of Fredholm integral equation solutions. [ABSTRACT FROM AUTHOR]

Fractal interpolation (FI) is widely used in nonlinear issues of natural and social sciences as it provides a constructive way to describe an irregular structure of data. A new approach of FI function (FIF) is proposed in this paper to represent uncertainty of irregular data. The proposed method is based on vertical shear factor instead of vertical scaling factor which is used in existing FI. Experiments were performed using existing datasets which confirmed the practical usefulness of the proposed method. A comparison with existing methods was also made to further verify the effectiveness of the proposed method. Furthermore, the criteria of the perturbed iterated function system (IFS) is proposed in order to satisfy the FI conditions and was explained with the help of an example. In addition, the error estimation between two IFS using the proposed refined equation is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point theorems for non-self mappings, which solve the problem 1 in [1], satisfying special contractive conditions in complete metric spaces. [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.

Contraction mappings provide us with one of the major sources of fixed point theorems. In many mathematical models, the existence of a solution may often be described by the existence of a fixed point for a suitable map. Therefore, study of such mappings and fixed point results becomes well motivated in the setting of intuitionistic fuzzy normed linear spaces (IFNLSs) as well. In this paper, we define some new contraction mappings and establish fixed point theorems in a complete IFNLS. Our results unify and generalize several classical results existing in the literature. [ABSTRACT FROM AUTHOR]

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]

We first study the asymptotic behavior of infinite products of nonexpansive selfmappings of a star-shaped complete metric space which is not necessarily bounded. Using the notion of contractivity and the Baire category approach, we show that a typical (generic) sequence of nonexpansive mappings is contractive and generates infinite products which have the same asymptotic behavior. This result is then applied to certain classes of nonexpansive set-valued self-mappings of a closed and star-shaped subset of a Banach space. It is shown that in these classes most (in the sense of Baire category) mappings are contractive. In particular, we show that this fact is true for a certain class of compact-valued mappings. It follows that a generic mapping in this class has a fixed point. [ABSTRACT FROM AUTHOR]

In this paper we provide three new type of contractive conditions and establish fixed point theorems related to them in the setting of an intuitionistic fuzzy n-Banach space. Our results improve and generalize several classical results existing in literature. Several examples have been provided in support of non-triviality of our results. [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]

In this paper, taking into account the recent contractive technique, which was introduced by Wardowski [18], we present a fixed point theorem for F-contractive type fuzzy mappings over a complete metric space. [ABSTRACT FROM AUTHOR]

In the framework of 2-metric spaces, a new class of square contractive conditions were established and the existence and uniqueness of the coupled common fixed point in given conditions were discussed, by means of the co-compatible condition for the pair of mappings. Then a new coupled common fixed point theorem was proved. Several illustrative examples were also given in support of the new theorem. The work improves the relative results in the re­cent literatures. [ABSTRACT FROM AUTHOR]

In the present paper a concept of $$C^*$$ -algebra-valued modular space is introduced which is a generalization of a modular space. Next, some fixed point theorems for self-maps with contractive or expansive conditions on such spaces are proved. [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 this paper, we introduce a new definition of Lipschitz-type continuity of a bifunction. Using this definition, we prove the contraction of the proximal mapping and apply it to the equilibrium problem over the fixed-point set of a nonexpansive mapping. We present a new algorithm for this problem. Under classical conditions, the convergence of the algorithm is proved. Finally, we present some numerical results for the proposed algorithm. [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]

In this paper, we prove the existence and uniqueness of solution for the fuzzy functional differential equation under generalized Hukuhara derivative via contractive-like mapping principles.

We study analytically and empirically the rate of convergence of two \(k\)-step fixed point iterative methods in the family of methods \[ x_{n+1}=T(x_{i_0+n-k+1},x_{i_1+n-k+1},\dots, x_{{i_{k-1}+n-k+1}}),\,n\geq k-1, \] where \(T\colon X^k\rightarrow X\) is a mapping satisfying some Presic type contraction conditions and \((i_0,i_1,\dots,i_{k-1})\) is a permutation of \((0,1,\dots,k-1)\). We also consider the Picard iteration associated to the fixed point problem \(x=T(x,\dots,x)\) and compare analytically and empirically the rate and speed of convergence of the three iterative methods. Our approach opens a new perspective on the study of the rate of convergence / speed of convergence of fixed point iterative methods and also illustrates the essential difference between them by means of some concrete numerical experiments.

Hasegawa, Kawasaki and Kobayashi [Fixed point theorems for contractively widely more generalized hybrid mappings in metric spaces, to appear in Linear and Nonlinear Anal.] introduced the concept of contractively widely more generalized hybrid mappings in a metric space. On the other hand, Bogin [A generalization of a fixed point theorem of Goebel, Kirk and Shimi, Canad. Math. Bull. 19 (1976) 7-12] showed a fixed point theorem. However, Bogin's result is not included in our results. In this paper, we consider new sufficient conditions as to cover the Bogin's fixed point theorem for contractively widely more generalized hybrid mappings to have a fixed point. [ABSTRACT FROM AUTHOR]

The aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi:]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler-Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new class of generalized metric spaces (called RS-spaces) that unify and extend, at the same time, Branciari's generalized metric spaces and Jleli and Samet's generalized metric spaces. Both families of spaces seen to be different in nature: on the one hand, Branciari's spaces are endowed with a rectangular inequality and their metrics are finite valued, but they can contain convergent sequences with two different limits, or convergent sequences that are not Cauchy; on the other hand, in Jleli and Samet's spaces, although the limit of a convergent sequence is unique, they are not endowed with a triangular inequality and we can found two points at infinite distance. However, we overcome such drawbacks and we illustrate that many abstract metric spaces (like dislocated metric spaces, b-metric spaces, rectangular metric spaces, modular metric spaces, among others) can be seen as particular cases of RS-spaces. In order to show its great applicability, we present some fixed point theorems in the setting of RS-spaces that extend well-known results in this line of research. [ABSTRACT FROM AUTHOR]

In this paper, an iterative algorithm for finding a common point of the set of zeros of an accretive operator and the set of fixed points of a nonexpansive mapping is considered in a uniformly convex Banach space having a weakly continuous duality mapping. Under suitable control conditions, strong convergence of the sequence generated by proposed algorithm to a common point of two sets is established. The main theorems develop and complement the recent results announced by researchers in this area. [ABSTRACT FROM AUTHOR]